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1.

図書
図書
1. Sieves in number theory
George Greaves
出版情報: Berlin ; Tokyo : Springer, c2001  xii, 304 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 43
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Introduction
The Structure of Sifting Arguments / 1：
The Sieves of Eratosthenes and Legendre / 1.1：
The Contribution of Eratosthenes / 1.1.1：
Legendre's Sieve / 1.1.2：
An Estimate for n(X) / 1.1.3：
The Distribution of Primes / 1.1.4：
Examples of Sifting Situations / 1.2：
Notations / 1.2.1：
The Integers in an Interval (Y - X, Y ) / 1.2.2：
Numbers Given by Polynomial Expressions / 1.2.3：
Arithmetic Progressions / 1.2.4：
Sums of Two Squares / 1.2.5：
Polynomials with Prime Arguments / 1.2.6：
A General Formulation of a Sifting Situation / 1.3：
The Basic Formulation / 1.3.1：
Legendre's Sieve in a General Setting / 1.3.2：
A Generalised Formulation / 1.3.3：
A Further Generalisation / 1.3.4：
Sifting Density / 1.3.5：
The Sifting Limit Β(k) / 1.3.6：
Composition of Sieves / 1.3.7：
Notes on Chapter 1 / 1.4：
Selberg's Upper Bound Method / 2：
The Sifting Apparatus / 2.1：
Selberg's Theorem / 2.1.1：
The Numbers (lambda)(d) / 2.1.2：
A Simple Application / 2.1.3：
General Estimates of G(x) and E(D, P) / 2.2：
An Estimate by Rankin's Device / 2.2.1：
Asymptotic Formulas / 2.2.2：
The Error Term / 2.2.3：
Applications / 2.3：
Prime Twins and Goldbach's Problem / 2.3.1：
Polynomial Sequences / 2.3.3：
Notes on Chapter 2 / 2.4：
Combinatorial Methods / 3：
The Construction of Combinatorial Sieves / 3.1：
Preliminary Discussion of Brun's Ideas / 3.1.1：
Fundamental Inequalities and Identities / 3.1.2：
Buchstab's Identity / 3.1.3：
The Combinatorial Sieve Lemma / 3.1.4：
Brun's Pure Sieve / 3.2：
Inequalities and Identities / 3.2.1：
The "Pure Sieve" Theorem / 3.2.2：
A Corollary / 3.2.3：
Prime Twins / 3.2.4：
A Modern Edition of Brun's Sieve / 3.3：
Rosser's Choice of X / 3.3.1：
A Technical Estimate / 3.3.2：
A Simplifying Approximation / 3.3.3：
A Combinatorial Sieve Theorem / 3.3.4：
Brun's Version of his Method / 3.3.5：
Brun's Choice of x / 3.4.1：
The Estimations / 3.4.2：
The Result / 3.4.3：
Notes on Chapter 3 / 3.5：
Rosser's Sieve / 4：
Approximations by Continuous Functions / 4.1：
The Recurrence Relations / 4.1.1：
Partial Summation / 4.1.2：
The Leading Terms / 4.1.3：
The Functions F and f / 4.2：
The Difference-Differential Equations / 4.2.1：
The Adjoint Equation and the Inner Product / 4.2.2：
Solutions of the Adjoint Equation / 4.2.3：
Particular Values of F(s) and f(s) / 4.2.4：
Asymptotic Analysis as k -> $(infinity$) / 4.2.5：
The Convergence Problem / 4.3：
The Auxiliary Functions / 4.3.1：
Adjoints and Inner Products / 4.3.2：
The Case k
A Sieve Theorem Following Rosser / 4.4：
The Case k >/= 1/2: a First Result / 4.4.1：
Theorem 1 when k
An Improved Version of Proposition 1 / 4.4.3：
A Two-Sided Estimate / 4.4.4：
Extremal Examples / 4.5：
The Linear Case / 4.5.1：
The Case k=1/2 / 4.5.2：
Notes on Chapter 4 / 4.6：
The Sieve with Weights / 5：
Simpler Weighting Devices / 5.1：
Logarithmic Weights / 5.1.1：
Modified Logarithmic Weights / 5.1.2：
Some Applications / 5.1.3：
More Elaborate Weighted Sieves / 5.2：
An Improved Weighting Device / 5.2.1：
Buchstab's Weights / 5.2.2：
A Weighted Sieve Following Rosser / 5.3：
Combining Sieving and Weighting / 5.3.1：
The Reduction Identities / 5.3.2：
An Identity for the Main Term / 5.3.3：
The Estimate for the Main Term / 5.3.4：
Notes on Chapter 5 / 5.4：
The Remainder Term in the Linear Sieve / 6：
The Bilinear Nature of Rosser's Construction / 6.1：
The Factorisation of x.d / 6.1.1：
Discretisations of Rosser's Sieve / 6.1.2：
Specification of Details / 6.1.3：
The Leading Contributions to the Main Term / 6.1.4：
The Remainder Term / 6.1.5：
Sifting Short Intervals / 6.2：
The Smoothed Formulation / 6.2.1：
The Remainder Sums / 6.2.2：
Trigonometrical Sums / 6.2.3：
Notes on Chapter 6 / 6.3：
Lower Bound Sieves when k > 1 / 7：
An Extension of Selberg's Upper Bound / 7.1：
The Integral Equation and the Function $(sigma$) (s) / 7.1.1：
The Estimation of G(s) / 7.1.2：
A Lower Bound Sieve via Buchstab's Identity / 7.2：
Buchstab's Iterations / 7.2.1：
The Buchstab Transform of the $(lambda$)2 Method / 7.2.2：
The Sifting Limit as k -> $(infinity$) / 7.2.3：
Selberg's a2 a" Method / 7.3：
The Improved Sifting Limit for Large k / 7.3.1：
Notes on Chapter 7 / 7.4：
References
Index
Introduction
The Structure of Sifting Arguments / 1：
The Sieves of Eratosthenes and Legendre / 1.1：
2.

図書
図書
2. Nonlinear diffusion equations
Zhuoqun Wu ... [et al.]
出版情報: Singapore : World Scientific, c2001  xvii, 502 p. ; 23 cm
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Preface
Newtonian Filtration Equations / Chapter 1：
Introduction / 1.1：
Physical examples / 1.1.1：
Definitions of generalized solutions / 1.1.2：
Special solutions / 1.1.3：
Existence and Uniqueness of Solutions: One Dimensional Case / 1.2：
Uniqueness of solutions / 1.2.1：
Existence of solutions / 1.2.2：
Comparison theorems / 1.2.3：
Some extensions / 1.2.4：
Existence and Uniqueness of Solutions: Higher Dimensional Case / 1.3：
Comparison theorem and uniqueness of solutions / 1.3.1：
Regularity of Solutions: One Dimensional Case / 1.3.2：
Lemma / 1.4.1：
Regularity of solutions / 1.4.2：
Regularity of Solutions: Higher Dimensional Case / 1.4.3：
Generalized class B[subscript 2] / 1.5.1：
Some lemmas / 1.5.2：
Properties of functions in the generalized class B[subscript 2] / 1.5.3：
Holder continuity of solutions / 1.5.4：
Properties of the Free Boundary: One Dimensional Case / 1.6：
Finite propagation of disturbances / 1.6.1：
Localization and extinction of disturbances / 1.6.2：
Differential equation on the free boundary / 1.6.3：
Continuously differentiability of the free boundary / 1.6.4：
Some further results / 1.6.5：
Properties of the Free Boundary: Higher Dimensional Case / 1.7：
Monotonicity and Holder continuity of the free boundary / 1.7.1：
Lipschitz continuity of the free boundary / 1.7.2：
Initial Trace of Solutions / 1.7.3：
Harnack inequality / 1.8.1：
Main result / 1.8.2：
Extension of existence and uniqueness theorem / 1.8.3：
Other Problems / 1.9：
Equations with strongly nonlinear sources / 1.9.1：
Asymptotic properties of solutions / 1.9.2：
Non-Newtonian Filtration Equations / Chapter 2：
Introduction Preliminary Knowledge / 2.1：
Introduction Physical example / 2.1.1：
Basic spaces and some lemmas / 2.1.2：
Existence of Solutions / 2.1.3：
The case u[subscript 0] [set membership] C[superscript [infinity] subscript 0](R[superscript N]) or u[subscript 0] [set membership] L[superscript 1](R[superscript N]) [intersection of] L[superscript [infinity](R[superscript N]) / 2.2.1：
The case u[subscript 0] [set membership] L[superscript 1 subscript loc](R[superscript N]) / 2.2.2：
Some remarks / 2.2.3：
Harnack Inequality and the Initial Trace of Solutions / 2.3：
Local Harnack inequality / 2.3.1：
Global Harnack inequality / 2.3.2：
Initial trace of solutions / 2.3.3：
Regularity of Solutions / 2.4：
Boundedness of solutions / 2.4.1：
Boundedness of the gradient of solutions / 2.4.2：
Holder continuity of the gradient of solutions / 2.4.3：
Uniqueness of Solutions / 2.5：
Auxiliary propositions / 2.5.1：
Uniqueness theorem and its proof / 2.5.2：
Properties of the Free Boundary / 2.6：
p-Laplacian equation with strongly nonlinear sources / 2.6.1：
General Quasilinear Equations of Second Order / 2.7.2：
Weakly Degenerate Equations in One Dimension / 3.1：
Uniqueness of bounded and measurable solutions / 3.2.1：
Existence of continuous solutions / 3.2.2：
Weakly Degenerate Equations in Higher Dimension / 3.2.3：
Existence of continuous solutions for equations with two points of degeneracy / 3.3.1：
Uniqueness of BV solutions / 3.3.2：
Existence of BV solutions / 3.3.3：
Strongly Degenerate Equations in One Dimension / 3.3.4：
Definitions of solutions with discontinuity / 3.4.1：
Interior discontinuity condition / 3.4.2：
Uniqueness of BV solutions of the Cauchy problem / 3.4.3：
Formulation of the boundary value problem / 3.4.4：
Boundary discontinuity condition / 3.4.5：
Uniqueness of BV solutions of the first boundary value problem / 3.4.6：
Existence of BV solutions of the first boundary value problem / 3.4.7：
Equations with degeneracy at infinity / 3.4.8：
Properties of the curves of discontinuity / 3.4.10：
Degenerate Equations in Higher Dimension without Terms of Lower Order / 3.5：
Uniqueness of bounded and integrable solutions / 3.5.1：
A lemma on weak convergence / 3.5.2：
General Strongly Degenerate Equations in Higher Dimension / 3.5.3：
Appendix Classes BV and BV[subscript x] / 3.6.1：
Nonlinear Diffusion Equations of Higher Order / Chapter 4：
Similarity Solutions of a Fourth Order Equation / 4.1：
Definition of similarity solutions / 4.2.1：
Existence and uniqueness of global solutions of the Cauchy problem / 4.2.2：
Properties of solutions at zero points / 4.2.3：
Properties of unbounded solutions / 4.2.5：
Bounded solutions on the half line / 4.2.6：
Bounded solutions on the whole line / 4.2.7：
Properties of solutions in typical cases k = 1,2,3,4 / 4.2.8：
Behavior of similarity solutions as t [right arrow] 0[superscript +] / 4.2.9：
Equations with Double-Degeneracy / 4.3：
Weighted energy equality of solutions / 4.3.1：
Some auxiliary inequalities / 4.3.4：
Asymptotic behavior of solutions / 4.3.5：
Extinction of solutions at finite time / 4.3.7：
Nonexistence of nonnegative solutions / 4.3.8：
Infinite propagation case / 4.3.9：
Cahn-Hilliard Equation with Constant Mobility / 4.4：
Existence of classical solutions / 4.4.1：
Blowing-up of solutions / 4.4.2：
Global existence of solutions for small initial value / 4.4.3：
Cahn-Hilliard Equations with Positive Concentration Dependent Mobility / 4.5：
A modified Campanato space / 4.5.1：
Holder norm estimates for a linear problem / 4.5.2：
Zero potential case / 4.5.3：
General case / 4.5.4：
Thin Film Equation / 4.6：
Definition of generalized solutions / 4.6.1：
Approximate solutions / 4.6.2：
Nonnegativity of solutions / 4.6.3：
Zeros of nonnegative solutions / 4.6.5：
Monotonicity of the support of solutions / 4.6.6：
Cahn-Hilliard Equation with Degenerate Mobility / 4.7：
Models with degenerate mobility / 4.7.1：
Definition of physical solutions / 4.7.2：
Physical solutions / 4.7.3：
Bibliography
Preface
Newtonian Filtration Equations / Chapter 1：
Introduction / 1.1：
3.

図書
図書
3. Numerical bifurcation analysis for reaction-diffusion equations
Zhen Mei
出版情報: Berlin : Springer, c2000  xiv, 414 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 28
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Reaction-Diffusion Equations / 1：
Introduction / 1.1：
Bifurcations and Pattern Formations / 1.2：
Boundary Conditions / 1.3：
Continuation Methods / 2：
Parameterization of Solution Curves / 2.1：
Natural parameterization / 2.1.1：
Parameterization with arclength / 2.1.2：
Parameterization with pseudo-arclength / 2.1.3：
Local Parameterization of Solution Manifolds / 2.2：
Predictor-Corrector Methods / 2.3：
Euler-Newton method / 2.3.1：
A continuation-Lanczos algorithm / 2.3.2：
A continuation-Arnoldi algorithm / 2.3.3：
Computation of Multi-Dimensional Solution Manifolds / 2.4：
Detecting and Computing Bifurcation Points / 3：
Generic Bifurcation Points / 3.1：
One-parameter problems / 3.1.1：
Two-parameter problems / 3.1.2：
Test Functions / 3.2：
Test functions for turning points / 3.2.1：
Test functions for simple bifurcation point / 3.2.2：
Test functions for Hopf bifurcations / 3.2.3：
Minimally extended systems / 3.2.4：
Computing Simple Bifurcation Points / 3.3：
Simple bifurcation points / 3.3.1：
Extended systems / 3.3.2：
Newton-like methods / 3.3.3：
Rank-1 corrections for sparse problems / 3.3.4：
A numerical example / 3.3.5：
Computing Hopf Bifurcation Points / 3.4：
Hopf points / 3.4.1：
Newton method for extended systems / 3.4.2：
Branch Switching at Simple Bifurcation Points / 4：
Structure of Bifurcating Solution Branches / 4.1：
Behavior of the Linearized Operator / 4.2：
Euler-Newton Continuation / 4.3：
Branch Switching via Regularized Systems / 4.4：
Other Branch Switching Techniques / 4.5：
Bifurcation Problems with Symmetry / 5：
Basic Group Concepts / 5.1：
Equivariant Bifurcation Problems / 5.2：
Equivariant Branching Lemma / 5.3：
A Semi-linear Elliptic PDE on the Unite Square / 5.4：
Liapunov-Schmidt Method / 6：
Liapunov-Schmidt Reduction / 6.1：
Equivariance of the Reduced Bifurcation Equations / 6.2：
Derivatives and Taylor Expansion / 6.3：
Equivalence, Determinacy and Stability / 6.4：
Simple Bifurcation Points / 6.5：
Truncated Liapunov-Schmidt Method / 6.6：
Branch Switching at Multiple Bifurcation Points / 6.7：
Branch switching with prescribed tangents / 6.7.1：
Branch switching with scaling techniques / 6.7.2：
Corank-2 Problems with Dm-symmetry / 6.8：
Semilinear elliptic PDEs on a square / 6.8.1：
A semilinear elliptic PDE on a hexagon / 6.8.2：
Center Manifold Theory / 7：
Center Manifolds and Their Properties / 7.1：
Approximation of Center Manifolds / 7.2：
Symmetry and Normal Form / 7.3：
Hopf bifurcations / 7.4.1：
Waves in Reaction-Diffusion Equations / 7.5：
Oscillating waves / 7.5.1：
Long waves / 7.5.2：
Long time and large spatial behavior / 7.5.3：
A Bifurcation Function for Homoclinic Orbits / 8：
A Bifurcation Function / 8.1：
Approximation of Homoclinic Orbits / 8.2：
Solving the Adjoint Variational Problem / 8.3：
Preserving the inner product / 8.3.1：
Systems with continuous symmetries / 8.3.2：
The Approximate Bifurcation Function / 8.4：
Examples / 8.5：
Freire et al.'s circuit / 8.5.1：
Kuramoto-Sivashinsky equation / 8.5.2：
One-Dimensional Reaction-Diffusion Equations / 9：
Linear Stability Analysis / 9.1：
The general system / 9.2.1：
The Brusselator equations / 9.2.2：
Solution Branches at Double Bifurcations / 9.3：
The reflection symmetry and its induced action / 9.3.1：
(k,m) = (odd, odd) or (odd, even) / 9.3.2：
(k,m) = (even, even) / 9.3.3：
Central Difference Approximations / 9.3.4：
General systems / 9.4.1：
Numerical Results for the Brusselator Equations / 9.4.2：
The length <$>\ell = 1<$>, diffusion rates d1 = 1, d2 = 2 / 9.5.1：
The length <$>\ell = 10<$>, diffusion rates d1 = 1, d2 = 2 / 9.5.2：
Reaction-Diffusion Equations on a Square / 10：
D4-Symmetry / 10.1：
Eigenpairs of the Laplacian / 10.2：
Bifurcation Points / 10.3：
Steady state bifurcation points / 10.4.1：
Hopf bifurcation points / 10.4.2：
Mode Interactions / 10.5：
Steady/steady state mode interactions / 10.5.1：
Hopf/steady state mode interactions / 10.5.2：
Hopf/Hopf mode interactions / 10.5.3：
Kernels of Du G0 and <$>(D_u G_0)^{\ast}<$> / 10.6：
Simple and Double Bifurcations / 10.7：
Simple bifurcations / 10.8.1：
Double bifurcations induced by the D4 symmetries / 10.8.2：
Normal Forms for Hopf Bifurcations / 11：
Domain Symmetries and Their Extensions / 11.1：
Actions of D4 on the Center Eigenspace / 11.3：
The Normal Form / 11.4：
Analysis of the Normal Form / 11.5：
Odd parity / 11.5.1：
Even parity / 11.5.2：
Brusselator Equations / 11.6：
Linear stability analysis / 11.6.1：
Bifurcation scenario / 11.6.2：
Nonlinear degeneracy / 11.6.3：
Steady/Steady State Mode Interactions / 12：
Induced Actions / 12.1：
Interaction of Two D4-Modes / 12.2：
Interaction of two even modes / 12.2.1：
Interaction of an even mode with an odd mode / 12.2.2：
Interaction of two odd modes / 12.2.3：
Mode Interactions of Three Modes / 12.3：
Induced actions / 12.3.1：
Interactions of the modes (m,n,k) =(even, odd, odd) / 12.3.2：
Interactions of the modes (m,n,k) =(even, odd, even) / 12.3.3：
Interactions of Four Modes / 12.4：
Interactions of the modes (m, n, k, l) = (even, odd, even, odd) / 12.4.1：
Interactions of the modes (m, n, k, l) = (even, even, even, odd) / 12.4.2：
Reactions with Z2-Symmetry / 12.5：
Hopf/Steady State Mode Interactions / 13：
Normal Forms / 13.1：
Bifurcation Scenario / 13.4：
Calculations of the Normal Form / 13.5：
Homotopy of Boundary Conditions / 14：
Homotopy of boundary conditions / 14.1：
Boundary conditions for different components / 14.1.2：
Mixed boundary conditions along the sides / 14.1.3：
Dynamical boundary conditions / 14.1.4：
A Brief Review of Sturm-Liouville Theory / 14.2：
Laplacian with Robin Boundary Conditions / 14.3：
Variational Form / 14.4：
Continuity of Solutions along the Homotopy / 14.5：
Neumann and Dirichlet Problems / 14.6：
Properties of Eigenvalues / 14.7：
One-dimensional problems / 14.7.1：
Two-dimensional problems / 14.7.2：
Bifurcations along a Homotopy of BCs / 15：
Stability and Symmetries / 15.1：
Variations of Bifurcations along the Homotopy / 15.3：
(κ1, κ2) = (odd, even) or (even, odd) / 15.4.1：
(κ1, κ2) = (odd, odd) / 15.4.2：
(κ1, κ2) = (even, even) / 15.4.3：
A Numerical Example / 15.5：
Discretization with finite difference methods / 15.5.1：
Homotopy of (κ1(μ), κ2(μ)) from (1,2) to (2,3) / 15.5.2：
Homotopy of (κl(μ), κ2(μ)) from (1,3) to (2,4) / 15.5.3：
Homotopy of (κ1(μ), κ2(μ)) from (2,4) to (3,5) / 15.5.4：
Forced Symmetry-Breaking in BCs / 15.6：
Bifurcation points / 15.6.1：
Bifurcation scenarios / 15.6.2：
A Mode Interaction on a Homotopy of BCs / 16：
Symmetries and Normal Forms / 16.1：
Generic Bifurcation Behavior / 16.3：
Solutions with the modes φ1, φ2 / 16.3.1：
Pure φ3-mode solutions / 16.3.2：
Interactions of three modes / 16.3.3：
Scales of Solution Branches / 16.4：
Secondary Bifurcations / 16.5：
Secondary Hopf bifurcations / 16.5.1：
Truncated Bifurcation Equations / 16.6：
Derivatives with respect to homotopy parameter / 16.6.1：
Reduced Stability / 16.7：
Stability of solution branches at (0, λ1(μ),μ) / 16.7.1：
Stability of solution branches at (0, λ2(μ), μ) / 16.7.2：
Stability of solution branches at mode interaction / 16.7.3：
Solution branches along (0; λ1(μ),μ) / 16.8：
Solution branches along (0, λ2(μ),μ) / 16.8.2：
Mode interaction / 16.8.3：
Switching and continuation of solution branches / 16.8.4：
List of Figures
List of Tables
Bibliography
Index
Reaction-Diffusion Equations / 1：
Introduction / 1.1：
Bifurcations and Pattern Formations / 1.2：
4.

図書
図書
4. Wave Motion (: hard ; : pbk.)
J. Billingham, A. C. King
出版情報: Cambridge : Cambridge University Press, 2000  ix, 468 p. ; 23 cm
シリーズ名: Cambridge texts in applied mathematics
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Introduction
Linear Waves / Part 1：
Basic Ideas / 1：
Exercises
Waves on a Stretched String / 2：
Derivation of the Governing Equation / 2.1：
Standing Waves on Strings of Finite Length / 2.2：
D'Alembert's Solution for Strings of Infinite Length / 2.3：
Reflection and Transmission of Waves by Discontinuities in Density / 2.4：
A Single Discontinuity / 2.4.1：
Two Discontinuities: Impedance Matching / 2.4.2：
Sound Waves / 3：
Plane Waves / 3.1：
Acoustic Energy Transmission / 3.3：
Plane Waves In Tubes / 3.4：
Acoustic Waveguides / 3.5：
Reflection of a Plane Acoustic Wave by a Rigid Wall / 3.5.1：
A Planar Waveguide / 3.5.2：
A Circular Waveguide / 3.5.3：
Acoustic Sources / 3.6：
The Acoustic Source / 3.6.1：
Energy Radiated by Sources and Plane Waves / 3.6.2：
Radiation from Sources in a Plane Wall / 3.7：
Linear Water Waves / 4：
Derivation of the Governing Equations / 4.1：
Linear Gravity Waves / 4.2：
Progressive Gravity Waves / 4.2.1：
Standing Gravity Waves / 4.2.2：
The Wavemaker / 4.2.3：
The Extraction of Energy from Water Waves / 4.2.4：
The Effect of Surface Tension: Capillary--Gravity Waves / 4.3：
Edge Waves / 4.4：
Ship Waves / 4.5：
The Solution of Initial Value Problems / 4.6：
Shallow Water Waves: Linear Theory / 4.7：
The Reflection of Sea Swell by a Step / 4.7.1：
Wave Amplification at a Gently Sloping Beach / 4.7.2：
Wave Refraction / 4.8：
The Kinematics of Slowly Varying Waves / 4.8.1：
Wave Refraction at a Gently Sloping Beach / 4.8.2：
The Effect of Viscosity / 4.9：
Waves in Elastic Solids / 5：
Waves in an Infinite Elastic Body / 5.1：
One-Dimensional Dilatation Waves / 5.2.1：
One-Dimensional Rotational Waves / 5.2.2：
Plane Waves with General Orientation / 5.2.3：
Two-Dimensional Waves in Semi-infinite Elastic Bodies / 5.3：
Normally Loaded Surface / 5.3.1：
Stress-Free Surface / 5.3.2：
Waves in Finite Elastic Bodies / 5.4：
Flexural Waves in Plates / 5.4.1：
Waves in Elastic Rods / 5.4.2：
Torsional Waves / 5.4.3：
Longitudinal Waves / 5.4.4：
The Excitation and Propagation of Elastic Wavefronts / 5.5：
Wavefronts Caused by an Internal Line Force in an Unbounded Elastic Body / 5.5.1：
Wavefronts Caused by a Point Force on the Free Surface of a Semi-infinite Elastic Body / 5.5.2：
Electromagnetic Waves / 6：
Electric and Magnetic Forces and Fields / 6.1：
Electrostatics: Gauss's Law / 6.2：
Magnetostatics: Ampere's Law and the Displacement Current / 6.3：
Electromagnetic Induction: Farady's Law / 6.4：
Plane Electromagnetic Waves / 6.5：
Conductors and Insulators / 6.6：
Reflection and Transmission at Interfaces / 6.7：
Boundary Conditions at Interfaces / 6.7.1：
Reflection by a Perfect Conductor / 6.7.2：
Reflection and Refraction by Insulators / 6.7.3：
Waveguides / 6.8：
Metal Waveguides / 6.8.1：
Weakly Guiding Optical Fibres / 6.8.2：
Radiation / 6.9：
Scalar and Vector Potentials / 6.9.1：
The Electric Dipole / 6.9.2：
The Far Field of a Localised Current Distribution / 6.9.3：
The Centre Fed Linear Antenna / 6.9.4：
Nonlinear Waves / Part 2：
The Formation and Propagation of Shock Waves / 7：
Traffic Waves / 7.1：
Small Amplitude Disturbances of a Uniform State / 7.1.1：
The Nonlinear Initial Value Problem / 7.1.3：
The Speed of the Shock / 7.1.4：
Compressible Gas Dynamics / 7.2：
Some Essential Thermodynamics / 7.2.1：
Equations of Motion / 7.2.2：
Construction of the Characteristic Curves / 7.2.3：
The Rankine--Hugoniot Relations / 7.2.4：
Detonations / 7.2.5：
Nonlinear Water Waves / 8：
Nonlinear Shallow Water Waves / 8.1：
The Dam Break Problem / 8.1.1：
A Shallow Water Bore / 8.1.2：
The Effect of Nonlinearity on Deep Water Gravity Waves: Stokes' Expansion / 8.2：
The Korteweg-de Vries Equation for Shallow Water Waves: the Interaction of Nonlinear Steepening and Linear Dispersion / 8.3：
Derivation of the Korteweg-de Vries Equation / 8.3.1：
Travelling Wave Solutions of the KdV Equation / 8.3.2：
Nonlinear Capillary Waves / 8.4：
Chemical and Electrochemical Waves / 9：
The Law of Mass Action / 9.1：
Molecular Diffusion / 9.2：
Reaction-Diffusion Systems / 9.3：
Autocatalytic Chemical Waves with Unequal Diffusion Coefficients* / 9.4：
Existence of Travelling Wave Solutions / 9.4.1：
Asymptotic Solution for [delta] [[ 1 / 9.4.2：
The Transmission of Nerve Impulses: the Fitzhugh-Nagumo Equations / 9.5：
The Fitzhugh-Nagumo Model / 9.5.1：
The Existence of a Threshold / 9.5.2：
Travelling Waves / 9.5.3：
Advanced Topics / Part 3：
Burgers' Equation: Competition between Wave Steepening and Wave Spreading / 10：
Burgers' Equation for Traffic Flow / 10.1：
The Effect of Dissipation on Weak Shock Waves in an Ideal Gas / 10.2：
Simple Solutions of Burgers' Equation / 10.3：
Asymptotic Solutions for v [[ 1 / 10.3.1：
Diffraction and Scattering / 11：
Diffraction of Acoustic Waves by a Semi-infinite Barrier / 11.1：
Preliminary Estimates of the Potential / 11.1.1：
Pre-transform Considerations / 11.1.2：
The Fourier Transform Solution / 11.1.3：
The Diffraction of Waves by an Aperture / 11.2：
Scalar Diffraction: Acoustic Waves / 11.2.1：
Vector Diffraction: Electromagnetic Waves / 11.2.2：
Scattering of Linear, Deep Water Waves by a Surface Piercing Cylinder / 11.3：
Solitons and the Inverse Scattering Transform / 12：
The Korteweg-de Vries Equation / 12.1：
The Scattering Problem / 12.1.1：
The Inverse Scattering Problem / 12.1.2：
Scattering Data for KdV Potentials / 12.1.3：
Examples: Solutions of the KdV Equation / 12.1.4：
The Nonlinear Schrodinger Equation / 12.2：
Derivation of the Nonlinear Schrodinger Equation for Plane Electromagnetic Waves / 12.2.1：
Solitary Wave Solutions of the Nonlinear Schrodinger Equation / 12.2.2：
The Inverse Scattering Transform for the Nonlinear Schrodinger Equation / 12.2.3：
Useful Mathematical Formulas and Physical Data / Appendix 1：
Cartesian Coordinates / A1.1：
Cylindrical Polar Coordinates / A1.2：
Spherical Polar Coordinates / A1.3：
Some Vector Calculus Identities and Useful Results for Smooth Vector Fields / A1.4：
Physical constants / A1.5：
Bibliography
Index
Introduction
Linear Waves / Part 1：
Basic Ideas / 1：
5.

図書
図書
5. 岩波講座基礎数学 (総索引 ; 月報 ; 月報(第3次))
小平邦彦監修 ; 岩堀長慶 [ほか] 編
出版情報: 東京 : 岩波書店, 1976.5-  冊 ; 22cm
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6.

図書
図書
6. Perturbation methods
Ali Hasan Nayfeh
出版情報: New York : Wiley, c1973  xii, 425 p. ; 23 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Introduction / 1.：
Parameter Perturbations / 1.1.：
An Algebraic Equation / 1.1.1.：
The van der Pol Oscillator / 1.1.2.：
Coordinate Perturbations / 1.2.：
The Bessel Equation of Zeroth Order / 1.2.1.：
A Simple Example / 1.2.2.：
Order Symbols and Gauge Functions / 1.3.：
Asymptotic Expansions and Sequences / 1.4.：
Asymptotic Series / 1.4.1.：
Asymptotic Expansions / 1.4.2.：
Uniqueness of Asymptotic Expansions / 1.4.3.：
Convergent versus Asymptotic Series / 1.5.：
Nonuniform Expansions / 1.6.：
Elementary Operations on Asymptotic Expansions / 1.7.：
Exercises
Straightforward Expansions and Sources of Nonuniformity / 2.：
Infinite Domains / 2.1.：
The Duffing Equation / 2.1.1.：
A Model for Weak Nonlinear Instability / 2.1.2.：
Supersonic Flow Past a Thin Airfoil / 2.1.3.：
Small Reynolds Number Flow Past a Sphere / 2.1.4.：
A Small Parameter Multiplying the Highest Derivative / 2.2.：
A Second-Order Example / 2.2.1.：
High Reynolds Number Flow Past a Body / 2.2.2.：
Relaxation Oscillations / 2.2.3.：
Unsymmetrical Bending of Prestressed Annular Plates / 2.2.4.：
Type Change of a Partial Differential Equation / 2.3.：
Long Waves on Liquids Flowing down Incline Planes / 2.3.1.：
The Presence of Singularities / 2.4.：
Shift in Singularity / 2.4.1.：
The Earth-Moon-Spaceship Problem / 2.4.2.：
Thermoelastic Surface Waves / 2.4.3.：
Turning Point Problems / 2.4.4.：
The Role of Coordinate Systems / 2.5.：
The Method of Strained Coordinates / 3.：
The Method of Strained Parameters / 3.1.：
The Lindstedt-Poincare Method / 3.1.1.：
Transition Curves for the Mathieu Equation / 3.1.2.：
Characteristic Exponents for the Mathieu Equation (Whittaker's Method) / 3.1.3.：
The Stability of the Triangular Points in the Elliptic Restricted Problem of Three Bodies / 3.1.4.：
Characteristic Exponents for the Triangular Points in the Elliptic Restricted Problem of Three Bodies / 3.1.5.：
A Simple Linear Eigenvalue Problem / 3.1.6.：
A Quasi-Linear Eigenvalue Problem / 3.1.7.：
The Quasi-Linear Klein-Gordon Equation / 3.1.8.：
Lighthill's Technique / 3.2.：
A First-Order Differential Equation / 3.2.1.：
The One-Dimensional Earth-Moon-Spaceship Problem / 3.2.2.：
A Solid Cylinder Expanding Uniformly in Still Air / 3.2.3.：
Expansions by Using Exact Characteristics--Nonlinear Elastic Waves / 3.2.4.：
Temple's Technique / 3.3.：
Renormalization Technique / 3.4.：
Limitations of the Method of Strained Coordinates / 3.4.1.：
The Methods of Matched and Composite Asymptotic Expansions / 3.5.1.：
The Method of Matched Asymptotic Expansions / 4.1.：
Introduction--Prandtl's Technique / 4.1.1.：
Higher Approximations and Refined Matching Procedures / 4.1.2.：
A Second-Order Equation with Variable Coefficients / 4.1.3.：
Reynolds' Equation for a Slider Bearing / 4.1.4.：
The Method of Composite Expansions / 4.1.5.：
A Second-Order Equation with Constant Coefficients / 4.2.1.：
An Initial Value Problem for the Heat Equation / 4.2.2.：
Limitations of the Method of Composite Expansions / 4.2.4.：
Variation of Parameters and Methods of Averaging / 5.：
Variation of Parameters / 5.1.：
Time-Dependent Solutions of the Schrodinger Equation / 5.1.1.：
A Nonlinear Stability Example / 5.1.2.：
The Method of Averaging / 5.2.：
Van der Pol's Technique / 5.2.1.：
The Krylov-Bogoliubov Technique / 5.2.2.：
The Generalized Method of Averaging / 5.2.3.：
Struble's Technique / 5.3.：
The Krylov-Bogoliubov-Mitropolski Technique / 5.4.：
The Duffiing Equation / 5.4.1.：
The Klein-Gordon Equation / 5.4.2.：
The Method of Averaging by Using Canonical Variables / 5.5.：
The Mathieu Equation / 5.5.1.：
A Swinging Spring / 5.5.3.：
Von Zeipel's Procedure / 5.6.：
Averaging by Using the Lie Series and Transforms / 5.6.1.：
The Lie Series and Transforms / 5.7.1.：
Generalized Algorithms / 5.7.2.：
Simplified General Algorithms / 5.7.3.：
A Procedure Outline / 5.7.4.：
Algorithms for Canonical Systems / 5.7.5.：
Averaging by Using Lagrangians / 5.8.：
A Model for Dispersive Waves / 5.8.1.：
A Model for Wave-Wave Interaction / 5.8.2.：
The Nonlinear Klein-Gordon Equation / 5.8.3.：
The Method of Multiple Scales / 6.：
Description of the Method / 6.1.：
Many-Variable Version (The Derivative-Expansion Procedure) / 6.1.1.：
The Two-Variable Expansion Procedure / 6.1.2.：
Generalized Method--Nonlinear Scales / 6.1.3.：
Applications of the Derivative-Expansion Method / 6.2.：
Forced Oscillations of the van der Pol Equation / 6.2.1.：
Parametric Resonances--The Mathieu Equation / 6.2.4.：
The van der Pol Oscillator with Delayed Amplitude Limiting / 6.2.5.：
Limitations of the Derivative-Expansion Method / 6.2.6.：
Limitations of This Technique / 6.3.：
Generalized Method / 6.4.：
A General Second-Order Equation with Variable Coefficients / 6.4.1.：
A Linear Oscillator with a Slowly Varying Restoring Force / 6.4.3.：
An Example with a Turning Point / 6.4.4.：
The Duffing Equation with Slowly Varying Coefficients / 6.4.5.：
Reentry Dynamics / 6.4.6.：
Advantages and Limitations of the Generalized Method / 6.4.7.：
Asymptotic Solutions of Linear Equations / 7.：
Second-Order Differential Equations / 7.1.：
Expansions Near an Irregular Singularity / 7.1.1.：
An Expansion of the Zeroth-Order Bessel Function for Large Argument / 7.1.2.：
Liouville's Problem / 7.1.3.：
Higher Approximations for Equations Containing a Large Parameter / 7.1.4.：
Homogeneous Problems with Slowly Varying Coefficients / 7.1.5.：
Reentry Missile Dynamics / 7.1.7.：
Inhomogeneous Problems with Slowly Varying Coefficients / 7.1.8.：
Successive Liouville-Green (WKB) Approximations / 7.1.9.：
Systems of First-Order Ordinary Equations / 7.2.：
Expansions Near an Irregular Singular Point / 7.2.1.：
Asymptotic Partitioning of Systems of Equations / 7.2.2.：
Subnormal Solutions / 7.2.3.：
Systems Containing a Parameter / 7.2.4.：
Homogeneous Systems with Slowly Varying Coefficients / 7.2.5.：
The Langer Transformation / 7.3.：
Problems with Two Turning Points / 7.3.3.：
Higher-Order Turning Point Problems / 7.3.4.：
Higher Approximations / 7.3.5.：
An Inhomogeneous Problem with a Simple Turning Point--First Approximation / 7.3.6.：
An Inhomogeneous Problem with a Simple Turning Point--Higher Approximations / 7.3.7.：
An Inhomogeneous Problem with a Second-Order Turning Point / 7.3.8.：
Turning Point Problems about Singularities / 7.3.9.：
Turning Point Problems of Higher Order / 7.3.10.：
Wave Equations / 7.4.：
The Born or Neumann Expansion and The Feynman Diagrams / 7.4.1.：
Renormalization Techniques / 7.4.2.：
Rytov's Method / 7.4.3.：
A Geometrical Optics Approximation / 7.4.4.：
A Uniform Expansion at a Caustic / 7.4.5.：
The Method of Smoothing / 7.4.6.：
References and Author Index
Subject Index
Introduction / 1.：
Parameter Perturbations / 1.1.：
An Algebraic Equation / 1.1.1.：
7.

図書
図書
7. Trigonometric series. 2nd ed (v. 1 ; v. 2)
A. Zygmund
出版情報: Cambridge : Cambridge University Press, 1959  2 v. (ix, 383, 354 p) ; 27 cm
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8.

図書
図書
8. Automorphic forms on SL[2](R)
Armand Borel
出版情報: Cambridge, U.K. ; New York, NY, USA : Cambridge University Press, 1997  x, 192 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 130
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目次情報: 続きを見る
Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane / Part I：
Prerequisites and notation / 1：
Review of SL2(R), differential operators, convolution / 2：
Action of G on X, discrete subgroups of G, fundamental domains / 3：
The unit disc model / 4：
Automorphic Forms and Cusp Forms / Part II：
Growth conditions, automorphic forms / 5：
Poincare series / 6：
Constant term:the fundamental estimate / 7：
Finite dimensionality of the space of automorphic forms of a given type / 8：
Convolution operators on cuspidal functions / 9：
Eisenstein Series / Part III：
Definition and convergence of Eisenstein series / 10：
Analytic continuation of the Eisenstein series / 11：
Eisenstein series and automorphic forms orthogonal to cusp forms / 12：
Spectral Decomposition and Representations / Part IV：
Spectral decomposition of L2(G G)m with respect to C / 13：
Generalities on representations of G / 14：
Representations of SL2(R) / 15：
Spectral decomposition of L2(G SL2(R)):the discrete spectrum / 16：
Spectral decomposition of L2(G SL2(R)): the continuous spectrum / 17：
Concluding remarks / 18：
Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane / Part I：
Prerequisites and notation / 1：
Review of SL2(R), differential operators, convolution / 2：
9.

図書
図書
9. Geometrical methods of mathematical physics (: pbk)
Bernard F. Schutz
出版情報: Cambridge ; New York : Cambridge University Press, 1980  xii, 250 p. ; 24 cm
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目次情報: 続きを見る
Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
Mappings / 1.2：
Real analysis / 1.3：
Group theory / 1.4：
Linear algebra / 1.5：
The algebra of square matrices / 1.6：
Bibliography / 1.7：
Differentiable manifolds and tensors / 2：
Definition of a manifold / 2.1：
The sphere as a manifold / 2.2：
Other examples of manifolds / 2.3：
Global considerations / 2.4：
Curves / 2.5：
Functions on M / 2.6：
Vectors and vector fields / 2.7：
Basis vectors and basis vector fields / 2.8：
Fiber bundles / 2.9：
Examples of fiber bundles / 2.10：
A deeper look at fiber bundles / 2.11：
Vector fields and integral curves / 2.12：
Exponentiation of the operator d/d[lambda] / 2.13：
Lie brackets and noncoordinate bases / 2.14：
When is a basis a coordinate basis? / 2.15：
One-forms / 2.16：
Examples of one-forms / 2.17：
The Dirac delta function / 2.18：
The gradient and the pictorial representation of a one-form / 2.19：
Basis one-forms and components of one-forms / 2.20：
Index notation / 2.21：
Tensors and tensor fields / 2.22：
Examples of tensors / 2.23：
Components of tensors and the outer product / 2.24：
Contraction / 2.25：
Basis transformations / 2.26：
Tensor operations on components / 2.27：
Functions and scalars / 2.28：
The metric tensor on a vector space / 2.29：
The metric tensor field on a manifold / 2.30：
Special relativity / 2.31：
Lie derivatives and Lie groups / 2.32：
Introduction: how a vector field maps a manifold into itself / 3.1：
Lie dragging a function / 3.2：
Lie dragging a vector field / 3.3：
Lie derivatives / 3.4：
Lie derivative of a one-form / 3.5：
Submanifolds / 3.6：
Frobenius' theorem (vector field version) / 3.7：
Proof of Frobenius' theorem / 3.8：
An example: the generators of S[superscript 2] / 3.9：
Invariance / 3.10：
Killing vector fields / 3.11：
Killing vectors and conserved quantities in particle dynamics / 3.12：
Axial symmetry / 3.13：
Abstract Lie groups / 3.14：
Examples of Lie groups / 3.15：
Lie algebras and their groups / 3.16：
Realizations and representations / 3.17：
Spherical symmetry, spherical harmonics and representations of the rotation group / 3.18：
Differential forms / 3.19：
The algebra and integral calculus of forms / A：
Definition of volume -- the geometrical role of differential forms / 4.1：
Notation and definitions for antisy mmetric tensors / 4.2：
Manipulating differential forms / 4.3：
Restriction of forms / 4.5：
Fields of forms / 4.6：
Handedness and orientability / 4.7：
Volumes and integration on oriented manifolds / 4.8：
N-vectors, duals, and the symbol [epsilon][subscript ij...k] / 4.9：
Tensor densities / 4.10：
Generalized Kronecker deltas / 4.11：
Determinants and [epsilon][subscript ij...k] / 4.12：
Metric volume elements / 4.13：
The differential calculus of forms and its applications / B：
The exterior derivative / 4.14：
Notation for derivatives / 4.15：
Familiar examples of exterior differentiation / 4.16：
Integrability conditions for partial differential equations / 4.17：
Exact forms / 4.18：
Proof of the local exactness of closed forms / 4.19：
Lie derivatives of forms / 4.20：
Lie derivatives and exterior derivatives commute / 4.21：
Stokes' theorem / 4.22：
Gauss' theorem and the definition of divergence / 4.23：
A glance at cohomology theory / 4.24：
Differential forms and differential equations / 4.25：
Frobenius' theorem (differential forms version) / 4.26：
Proof of the equivalence of the two versions of Frobenius' theorem / 4.27：
Conservation laws / 4.28：
Vector spherical harmonics / 4.29：
Applications in physics / 4.30：
Thermodynamics
Simple systems / 5.1：
Maxwell and other mathematical identities / 5.2：
Composite thermodynamic systems: Caratheodory's theorem / 5.3：
Hamiltonian mechanics
Hamiltonian vector fields / 5.4：
Canonical transformations / 5.5：
Map between vectors and one-forms provided by [characters not reproducible] / 5.6：
Poisson bracket / 5.7：
Many-particle systems: symplectic forms / 5.8：
Linear dynamical systems: the symplectic inner product and conserved quantities / 5.9：
Fiber bundle structure of the Hamiltonian equations / 5.10：
Electromagnetism / C：
Rewriting Maxwell's equations using differential forms / 5.11：
Charge and topology / 5.12：
The vector potential / 5.13：
Plane waves: a simple example / 5.14：
Dynamics of a perfect fluid / D：
Role of Lie derivatives / 5.15：
The comoving time-derivative / 5.16：
Equation of motion / 5.17：
Conservation of vorticity / 5.18：
Cosmology / E：
The cosmological principle / 5.19：
Lie algebra of maximal symmetry / 5.20：
The metric of a spherically symmetric three-space / 5.21：
Construction of the six Killing vectors / 5.22：
Open, closed, and flat universes / 5.23：
Connections for Riemannian manifolds and gauge theories / 5.24：
Introduction / 6.1：
Parallelism on curved surfaces / 6.2：
The covariant derivative / 6.3：
Components: covariant derivatives of the basis / 6.4：
Torsion / 6.5：
Geodesics / 6.6：
Normal coordinates / 6.7：
Riemann tensor / 6.8：
Geometric interpretation of the Riemann tensor / 6.9：
Flat spaces / 6.10：
Compatibility of the connection with volume-measure or the metric / 6.11：
Metric connections / 6.12：
The affine connection and the equivalence principle / 6.13：
Connections and gauge theories: the example of electromagnetism / 6.14：
Solutions and hints for selected exercises / 6.15：
Notation
Index
Appendix
Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
10.

図書
図書
10. Algebraic curves over finite fields
Carlos Moreno
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1991  ix, 246 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 97
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目次情報: 続きを見る
Preface
Algebraic curves and function fields / 1：
Geometric aspects / 1.1：
Introduction / 1.1.1：
Affine varieties / 1.1.2：
Projective varieties / 1.1.3：
Morphisms / 1.1.4：
Rational maps / 1.1.5：
Non-singular varieties / 1.1.6：
Smooth models of algebraic curves / 1.1.7：
Algebraic aspects / 1.2：
Points on the projective line P[superscript 1] / 1.2.1：
Extensions of valuation rings / 1.2.3：
Points on a smooth curve / 1.2.4：
Independence of valuations / 1.2.5：
Exercises
Notes
The Riemann-Roch theorem / 2：
Divisors / 2.1：
The vector space L(D) / 2.2：
Principal divisors and the group of divisor classes / 2.3：
The Riemann theorem / 2.4：
Pre-adeles (repartitions) / 2.5：
Pseudo-differentials (the Riemann-Roch theorem) / 2.6：
Zeta functions / 3：
The zeta functions of curves / 3.1：
The functional equation / 3.3：
Consequences of the functional equation / 3.3.1：
The Riemann hypothesis / 3.4：
The L-functions of curves and their functional equations / 3.5：
Preliminary remarks and notation / 3.5.1：
Exponential sums / 3.5.2：
The zeta function of the projective line / 4.1：
Gauss sums: first example of an L-function for the projective line / 4.2：
Properties of Gauss sums / 4.3：
Cyclotomic extensions: basic facts / 4.3.0：
Elementary properties / 4.3.1：
The Hasse-Davenport relation / 4.3.2：
Stickelberger's theorem / 4.3.3：
Kloosterman sums / 4.4：
Second example of an L-function for the projective line / 4.4.1：
A Hasse-Davenport relation for Kloosterman sums / 4.4.2：
Third example of an L-function for the projective line / 4.5：
Basic arithmetic theory of exponential sums / 4.6：
Part I: L-functions for the projective line / 4.6.1：
Part II: Artin-Schreier coverings / 4.6.2：
The Hurwitz-Zeuthen formula for the covering [pi]: C [right arrow] C / 4.6.3：
Goppa codes and modular curves / 5：
Elementary Goppa codes / 5.1：
The affine and projective lines / 5.2：
Affine line A[superscript 1](k) / 5.2.1：
Projective line P[superscript 1] / 5.2.2：
Goppa codes on the projective line / 5.3：
Algebraic curves / 5.4：
Separable extensions / 5.4.1：
Closed points and their neighborhoods / 5.4.2：
Differentials / 5.4.3：
The theorems of Riemann-Roch, of Hurwitz and of the Residue / 5.4.4：
Linear series / 5.4.6：
Algebraic geometric codes / 5.5：
Algebraic Goppa codes / 5.5.1：
Codes with better rates than the Varshamov-Gilbert bound / 5.5.2：
The theorem of Tsfasman, Vladut and Zink / 5.6：
Modular curves / 5.6.1：
Elliptic curves over C / 5.6.2：
Elliptic curves over the fields F[subscript p], Q / 5.6.3：
Torsion points on elliptic curves / 5.6.4：
Igusa's theorem / 5.6.5：
The modular equation / 5.6.6：
The congruence formula / 5.6.7：
The Eichler-Selberg trace formula / 5.6.8：
Proof of the theorem of Tsfasman, Vladut and Zink / 5.6.9：
Examples of algebraic Goppa codes / 5.7：
The Hamming (7,4) code / 5.7.1：
BCH codes / 5.7.2：
The Fermat cubic (Hermite form) / 5.7.3：
Elliptic codes (according to Driencourt-Michon) / 5.7.4：
The Klein quartic / 5.7.5：
Simplification of the singularities of algebraic curves / Appendix：
Homogeneous coordinates in the plane / A.1：
Basic lemmas / A.2：
Dual curves / A.3：
Plucker formulas / A.3.1：
Quadratic transformations / A.4：
Quadratic transform of a plane curve / A.4.1：
Quadratic transform of a singularity / A.4.2：
Singularities off the exceptional lines / A.4.3：
Reduction of singularities / A.4.4：
Bibliography
Index
Preface
Algebraic curves and function fields / 1：
Geometric aspects / 1.1：
11.

図書
図書
11. Torsors and rational points (: hbk)
Alexei Skorobogatov
出版情報: Cambridge : Cambridge University Press, 2001  viii, 187 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 144
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目次情報: 続きを見る
Introduction / 1：
Torsors / Part 1：
Torsors: general theory / 2：
Torsors over a field / 2.1：
Torsors and Cech cohomology / 2.2：
Torsors under groups of multiplicative type / 2.3：
Obstructions to existence of rational points over arbitrary fields / 2.4：
Examples of torsors / 3：
Torsors in geometric invariant theory / 3.1：
Classification of Del Pezzo surfaces of degree 5 / Appendix：
Homogeneous spaces and central extensions / 3.2：
Torsors under abelian varieties / 3.3：
Equations for 2- and 4-coverings of elliptic curves
Abelian torsors / 4：
From abelian torsors to Azumaya algebras / 4.1：
A commutative diagram / 4.2：
Local description of abelian torsors / 4.3：
Torsors associated with a dominant morphism to P[superscript 1 subscript k] / 4.4：
Descent and Manin Obstruction / Part 2：
Obstructions over number fields / 5：
The Hasse principle, weak and strong approximation / 5.1：
The Manin obstruction / 5.2：
Descent obstructions / 5.3：
Abelian descent and Manin obstruction / 6：
Descent theory / 6.1：
Manin obstruction and global duality pairings / 6.2：
Compactifications of torsors under tori / 6.3：
Abelian descent on conic bundle surfaces / 7：
Brauer group of conic bundles / 7.1：
Chatelet surfaces / 7.2：
Some intersections of two quadrics in P[superscript 5 subscript k] / 7.3：
Conic bundles with six singular fibres / 7.4：
Non-abelian descent on bielliptic surfaces / 8：
Beyond the Manin obstruction / 8.1：
An example of 4-torsion in III (E)
Interpretation in terms of non-abelian torsors / 8.2：
Homogeneous spaces and non-abelian cohomology / 9：
Liens and non-abelian H[superscript 2] / 9.1：
The Springer class of a homogeneous space / 9.2：
Abelianization of non-abelian H[superscript 2] / 9.3：
Hasse principle for non-abelian H[superscript 2] / 9.4：
Descent on homogeneous spaces / 9.5：
References
Index
Introduction / 1：
Torsors / Part 1：
Torsors: general theory / 2：
12.

図書
図書
12. Sample survey methods and theory (v. 1 ; v. 2)
by Morris H. Hansen, William N. Hurwitz and William G. Madow
出版情報: New York : Wiley, c1953  v. ; 23 cm
シリーズ名: Wiley publications in statistics
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目次情報:
Vol. 1. Methods and applications
Vol. 2. Theory
Vol. 1. Methods and applications
Vol. 2. Theory
13.

図書
図書
13. L[2]-invariants : theory and applications to geometry and K-theory
Wolfgang Lück
出版情報: Berlin ; Tokyo : Springer, c2002  xv, 595 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 44
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14.

図書
図書
14. Differential thermal analysis (v. 1 ; v. 2)
edited by R.C. Mackenzie
出版情報: London ; New York : Academic Press, 1970-1972  2 v. ; 24 cm
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15.

図書
図書
15. Fractal geometry : mathematical foundations and applications (: hbk ; : pbk)
Kenneth Falconer
出版情報: Chichester, West Sussex, England : Wiley, c1990  xxii, 288 p. ; 24 cm
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目次情報: 続きを見る
Preface
Preface to the second edition
Course suggestions
Introduction
Notes and references
Foundations / Part I：
Mathematical background / Chapter 1：
Basic set theory / 1.1：
Functions and limits / 1.2：
Measures and mass distributions / 1.3：
Notes on probability theory / 1.4：
Exercises / 1.5：
Hausdorff measure and dimension / Chapter 2：
Hausdorff measure / 2.1：
Hausdorff dimension / 2.2：
Calculation of Hausdorff dimension-simple examples / 2.3：
Equivalent definitions of Hausdorff dimension / 2.4：
Finer definitions of dimension / 2.5：
Alternative definitions of dimension / 2.6：
Box-counting dimensions / 3.1：
Properties and problems of box-counting dimension / 3.2：
Calculation of Hausdorff dimension--simple examples / 3.3：
Modified box-counting dimensions
Packing measures and dimensions / 3.4：
Some other definitions of dimension / 3.5：
Techniques for calculating dimensions / 3.6：
Basic methods / 4.1：
Subsets of finite measure / 4.2：
Potential theoretic methods / 4.3：
Fourier transform methods / 4.4：
Local structure of fractals / 4.5：
Densities / 5.1：
Structure of 1-sets / 5.2：
Tangents to s-sets / 5.3：
Projections of fractals / 5.4：
Projections of arbitrary sets / 6.1：
Projections of s-sets of integral dimension / 6.2：
Projections of arbitrary sets of integral dimension / 6.3：
Products of fractals / 6.4：
Product formulae / 7.1：
Intersections of fractals / 7.2：
Intersection formulae for fractals / 8.1：
Sets with large intersection / 8.2：
Applications and Examples / 8.3：
Iterated function systems-self-similar and self-affine sets / Chapter 9：
Iterated function system / 9.1：
Dimensions of self-similar sets / 9.2：
Some variations / 9.3：
Self-affine sets / 9.4：
Applications to encoding images / 9.5：
Examples from number theory / 9.6：
Distribution of digits of numbers / 10.1：
Continued fractions / 10.2：
Diophantine approximation / 10.3：
Graphs of functions / 10.4：
Dimensions of graphs / 11.1：
Autocorrelation of fractal functions / 11.2：
Examples from pure mathematics / 11.3：
Duality and the Kakeya problem / 12.1：
Vitushkin's conjecture / 12.2：
Convex functions / 12.3：
Groups and rings of fractional dimension / 12.4：
Dynamical systems / 12.5：
Repellers and iterated function systems / 13.1：
The logistic map / 13.2：
Stretching and folding transformations / 13.3：
The solenoid / 13.4：
Iterated function systems--self-similar and self-affine sets
Continuous dynamical systems / 13.5：
Iterated function systems / 13.6：
Small divisor theory
Liapounov exponents and entropies / 13.7：
Iteration of complex functions-Julia sets / 13.8：
General theory of Julia sets / 14.1：
Quadratic functions-the Mandelbrot set / 14.2：
Julia sets of quadratic functions / 14.3：
Characterization of quasi-circles by dimension / 14.4：
Newton's method for solving polynomial equations / 14.5：
Random fractals / 14.6：
A random Cantor set / 15.1：
Fractal percolation / 15.2：
Brownian motion and Brownian surfaces / 15.3：
Brownian motion / 16.1：
Fractional Brownian motion / 16.2：
Levy stable processes / 16.3：
Fractional Brownian surfaces / 16.4：
Multifractal measures / 16.5：
Coarse multifractal analysis / 17.1：
Fine multifractal analysis / 17.2：
Self-similar multifractals / 17.3：
Physical applications / 17.4：
Fractal growth / 18.1：
Singularities of electrostatic and gravitational potentials / 18.2：
Fluid dynamics and turbulence / 18.3：
Fractal antennas / 18.4：
Fractals in finance / 18.5：
References / 18.6：
Index
Iteration of complex functions--Julia sets
Quadratic functions--the Mandelbrot set
Preface
Preface to the second edition
Course suggestions
16.

図書
図書
16. Theoretical numerical analysis : an introduction to advanced techniques
Peter Linz
出版情報: New York : Wiley, c1979  xi, 228 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Basic Concepts / Part I：
Review of Functional Analysis / Chapter 1：
Linear Spaces / 1.1：
Norms / 1.2：
Banach and Hilbert Spaces / 1.3：
Mappings and Operators / 1.4：
Classification of Problems in Computational Mathematics / 1.5：
Approximation Theory / Chapter 2：
The General Interpolation Problem / 2.1：
Polynomial Interpolation / 2.2：
Piecewise Polynomial Approximations and Splines / 2.3：
Best Approximations in Inner Product Spaces / 2.4：
Best Approximations in the Maximum Norm / 2.5：
Approximations in Several Variables / 2.6：
Theoretical Aspects of Computational Mathematics / Part II：
Numerical Integration / Chapter 3：
Interpolatory Quadrature Rules / 3.1：
Product Integration / 3.2：
Another Approach to Numerical Integration / 3.3：
The Approximate Solution of Linear Operator Equations / Chapter 4：
Some Theorems on Linear Operators / 4.1：
Approximate Expansion Methods / 4.2：
Stability and Convergence / 4.3：
Error Estimates and Extrapolation / 4.4：
Approximate Computation of Eigenvalues / 4.5：
The Nonlinear Inverse Problem / Chapter 5：
The Method of Successive Substitutions / 5.1：
Some Elementary Results in the Calculus of Operators / 5.2：
The Generalized Newton's Method / 5.3：
The Minimization of Functionals / 5.4：
Special Topics / Part III：
The Approximate Solution of Linear Operator Equations of the Second Kind / Chapter 6：
Compact Operators and Equations of the Second Kind / 6.1：
The Method of Degenerate Kernels for Fredholm Equations / 6.2：
The Nystrom Method / 6.3：
Analysis of Methods for Integral Equations via Restrictions and Prolongations / 6.4：
General Operator Equations of the Second Kind / 6.5：
The Finite Element Method / Chapter 7：
Variational Formulation of Operator Equations and Galerkin's Method / 7.1：
The Construction of the Finite Elements / 7.2：
Convergence Rates for the Finite Element Method / 7.3：
Stability of the Finite Element Method / 7.4：
The Solution of Nonlinear Operator Equations by Discretization / Chapter 8：
Well-posedness and Condition Numbers / 8.1：
Asymptotic Expansions of the Discretization Error / 8.2：
The Solution of Improperly Posed Problems / Chapter 9：
Regularization Techniques / 9.1：
Expansion Methods / 9.2：
References
Index
Basic Concepts / Part I：
Review of Functional Analysis / Chapter 1：
Linear Spaces / 1.1：
17.

図書
図書
17. Quantum mechanics (v. 1 : hard - v. 2 : pbk)
Albert Messiah ; [translated from the French by G.M. Temmer]
出版情報: Amsterdam : North-Holland , New York : Sole dostributors for U.S.A., Intersicence Publishers, 1961-1962  2 v. (xv, 1136 p.) ; 22 cm
シリーズ名: Series in physics
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18.

図書
図書
18. The special functions and their approximations (v. 1 ; v. 2)
Yudell L. Luke
出版情報: New York : Academic Press, 1969  2 v. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 53
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19.

図書
図書
19. Lehrbuch der Funktionentheorie. 2nd ed., Rep. (Bd. 2)
von W. F. Osgood
出版情報: Bronx, N. Y. : Chelsea Pub. Co., 1965  xiv, 686 p. ; 21 cm
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20.

図書
図書
20. 高等数学教程 (1 : 1巻第1分冊 - 12 : 5巻第2分冊)
スミルノフ [著] ; 彌永昌吉 [ほか] 飜訳監修 ; 福原満洲雄訳者代表
出版情報: 東京 : 共立出版, 1958.5-1962.10  12冊 ; 22cm
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21.

図書
図書
21. Algebra. 5. Aufl. der Modernen Algebra (2)
B.L. van der Waerden, unter Benutzung von Vorlesungen von E. Artin und E. Noether
出版情報: Berlin ; New York : Springer-Verlag, 1967  v. ; 21 cm
シリーズ名: Heidelberger Taschenbücher ; Bd. 23
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22.

図書
図書
22. 数論 (1 ; 2 ; 3)
河田敬義著
出版情報: 東京 : 岩波書店, 1978.2-1979.2  3冊 (432p) ; 21cm
シリーズ名: 岩波講座基礎数学 / 小平邦彦監修 ; 岩堀長慶 [ほか] 編 ; 7 . 代数学||ダイスウガク ; 6
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23.

図書
図書
23. Celestial mechanics (pt. 1 : cloth - pt. 2 : pbk)
Shlomo Sternberg
出版情報: New York : W.A. Benjamin, 1969  2 v. ; 23 cm
シリーズ名: Mathematics lecture note series
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24.

図書
図書
24. Eigenfunction expansions associated with second-order differential equations ([pt. 1] ; pt. 2)
by E.C. Titchmarsh
出版情報: Oxford : Clarendon Press, 1946-1958  2 v. ; 25 cm
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25.

図書
図書
25. A course in probability theory. 2nd ed
Kai Lai Chung
出版情報: New York ; Tokyo : Academic Press, c1974  xii, 365 p. ; 23 cm
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks ; 21
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目次情報: 続きを見る
Preface to the third edition
Preface to the second edition
Preface to the first edition
Distribution function / 1：
Monotone functions / 1.1：
Distribution functions / 1.2：
Absolutely continuous and singular distributions / 1.3：
Measure theory / 2：
Classes of sets / 2.1：
Probability measures and their distribution functions / 2.2：
Random variable. Expectation. Independence / 3：
General definitions / 3.1：
Properties of mathematical expectation / 3.2：
Independence / 3.3：
Convergence concepts / 4：
Various modes of convergence / 4.1：
Almost sure convergence; Borel-Cantelli lemma / 4.2：
Vague convergence / 4.3：
Continuation / 4.4：
Uniform integrability; convergence of moments / 4.5：
Law of large numbers. Random series / 5：
Simple limit theorems / 5.1：
Weak law of large numbers / 5.2：
Convergence of series / 5.3：
Strong law of large numbers / 5.4：
Applications / 5.5：
Bibliographical Note
Characteristic function / 6：
General properties; convolutions / 6.1：
Uniqueness and inversion / 6.2：
Convergence theorems / 6.3：
Simple applications / 6.4：
Representation theorems / 6.5：
Multidimensional case; Laplace transforms / 6.6：
Central limit theorem and its ramifications / 7：
Liapounov's theorem / 7.1：
Lindeberg-Feller theorem / 7.2：
Ramifications of the central limit theorem / 7.3：
Error estimation / 7.4：
Law of the iterated logarithm / 7.5：
Infinite divisibility / 7.6：
Random walk / 8：
Zero-or-one laws / 8.1：
Basic notions / 8.2：
Recurrence / 8.3：
Fine structure / 8.4：
Conditioning. Markov property. Martingale / 8.5：
Basic properties of conditional expectation / 9.1：
Conditional independence; Markov property / 9.2：
Basic properties of smartingales / 9.3：
Inequalities and convergence / 9.4：
Supplement: Measure and Integral / 9.5：
Construction of measure
Characterization of extensions
Measures in R
Integral
General Bibliography
Index
Preface to the third edition
Preface to the second edition
Preface to the first edition
26.

図書
図書
26. Nonlinear dynamics and chaos. 2nd ed (: pbk)
J.M.T. Thompson and H.B. Stewart
出版情報: Chichester [West Sussex] : Wiley, c2002  xxii, 437 p. ; 23 cm
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目次情報: 続きを見る
Preface
Preface to the First Edition
Acknowledgements from the First Edition
Introduction / 1：
Historical background / 1.1：
Chaotic dynamics in Duffing's oscillator / 1.2：
Attractors and bifurcations / 1.3：
Basic Concepts of Nonlinear Dynamics / Part I：
An overview of nonlinear phenomena / 2：
Undamped, unforced linear oscillator / 2.1：
Undamped, unforced nonlinear oscillator / 2.2：
Damped, unforced linear oscillator / 2.3：
Damped, unforced nonlinear oscillator / 2.4：
Forced linear oscillator / 2.5：
Forced nonlinear oscillator: periodic attractors / 2.6：
Forced nonlinear oscillator: chaotic attractor / 2.7：
Point attractors in autonomous systems / 3：
The linear oscillator / 3.1：
Nonlinear pendulum oscillations / 3.2：
Evolving ecological systems / 3.3：
Competing point attractors / 3.4：
Attractors of a spinning satellite / 3.5：
Limit cycles in autonomous systems / 4：
The single attractor / 4.1：
Limit cycle in a neural system / 4.2：
Bifurcations of a chemical oscillator / 4.3：
Multiple limit cycles in aeroelastic galloping / 4.4：
Topology of two-dimensional phase space / 4.5：
Periodic attractors in driven oscillators / 5：
The Poincare map / 5.1：
Linear resonance / 5.2：
Nonlinear resonance / 5.3：
The smoothed variational equation / 5.4：
Variational equation for subharmonics / 5.5：
Basins of attraction by mapping techniques / 5.6：
Resonance of a self-exciting system / 5.7：
The ABC of nonlinear dynamics / 5.8：
Chaotic attractors in forced oscillators / 6：
Relaxation oscillations and heartbeat / 6.1：
The Birkhoff-Shaw chaotic attractor / 6.2：
Systems with nonlinear restoring force / 6.3：
Stability and bifurcations of equilibria and cycles / 7：
Liapunov stability and structural stability / 7.1：
Centre manifold theorem / 7.2：
Local bifurcations of equilibrium paths / 7.3：
Local bifurcations of cycles / 7.4：
Basin changes at local bifurcations / 7.5：
Prediction of incipient instability / 7.6：
Iterated Maps as Dynamical Systems / Part II：
Stability and bifurcation of maps / 8：
Stability of one-dimensional maps / 8.1：
Bifurcations of one-dimensional maps / 8.3：
Stability of two-dimensional maps / 8.4：
Bifurcations of two-dimensional maps / 8.5：
Basin changes at local bifurcations of limit cycles / 8.6：
Chaotic behaviour of one- and two-dimensional maps / 9：
General outline / 9.1：
Theory for one-dimensional maps / 9.2：
Bifurcations to chaos / 9.3：
Bifurcation diagram of one-dimensional maps / 9.4：
Henon map / 9.5：
Flows, Outstructures, and Chaos / Part III：
The geometry of recurrence / 10：
Finite-dimensional dynamical systems / 10.1：
Types of recurrent behaviour / 10.2：
Hyperbolic stability types for equilibria / 10.3：
Hyperbolic stability types for limit cycles / 10.4：
Implications of hyperbolic structure / 10.5：
The Lorenz system / 11：
A model of thermal convection / 11.1：
First convective instability / 11.2：
The chaotic attractor of Lorenz / 11.3：
Geometry of a transition to chaos / 11.4：
Rossler's band / 12：
The simply folded band in an autonomous system / 12.1：
Return map and bifurcations / 12.2：
Smale's horseshoe map / 12.3：
Transverse homoclinic trajectories / 12.4：
Spatial chaos and localized buckling / 12.5：
Geometry of bifurcations / 13：
Local bifurcations / 13.1：
Global bifurcations in the phase plane / 13.2：
Bifurcations of chaotic attractors / 13.3：
Applications in the Physical Sciences / Part IV：
Subharmonic resonances of an offshore structure / 14：
Basic equation and non-dimensional form / 14.1：
Analytical solution for each domain / 14.2：
Digital computer program / 14.3：
Resonance response curves / 14.4：
Effect of damping / 14.5：
Computed phase projections / 14.6：
Multiple solutions and domains of attraction / 14.7：
Chaotic motions of an impacting system / 15：
Resonance response curve / 15.1：
Application to moored vessels / 15.2：
Period-doubling and chaotic solutions / 15.3：
Escape from a potential well / 16：
Analytical formulation / 16.1：
Overview of the steady-state response / 16.3：
The two-band chaotic attractor / 16.4：
Resonance of the steady states / 16.5：
Transients and basins of attraction / 16.6：
Homoclinic phenomena / 16.7：
Heteroclinic phenomena / 16.8：
Indeterminate bifurcations / 16.9：
Appendix
Illustrated Glossary
Bibliography
Online Resources
Index
Preface
Preface to the First Edition
Acknowledgements from the First Edition
27.

図書
図書
27. 群論 (1 ; 2)
ア・ゲ・クローシュ著 ; 吉崎敬夫訳
出版情報: 東京 : 商工出版社, 1960-1961  2冊 ; 22cm
シリーズ名: 数学選書
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28.

図書
図書
28. 数学史 (1 ; 2)
コールマン, ユシケービッチ著 ; 山内一次, 井関清志訳
出版情報: 東京 : 東京図書, 1970-1971  2冊 ; 22cm
シリーズ名: 数学選書
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29.

図書
図書
29. An introduction to wavelets through linear algebra
Michael W. Frazier
出版情報: New York ; Tokyo : Springer, c1999  xvi, 501 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
Background: Complex Numbers and Linear Algebra / 1：
Real Numbers and Complex Numbers / 1.1：
Complex Series, Euler's Formula, and the Roots of Unity / 1.2：
Vector Spaces and Bases / 1.3：
Linear Transformations, Matrices, and Change of Basis / 1.4：
Diagonalization of Linear Transformations and Matrices / 1.5：
Inner Products, Orthonormal Bases, and Unitary Matrices / 1.6：
The Discrete Fourier Transform / 2：
Basic Properties of the Discrete Fourier Transform / 2.1：
Translation-Invariant Linear Transformations / 2.2：
The Fast Fourier Transform / 2.3：
Wavelets on $bZ_N$ / 3：
Construction of Wavelets on $bZ_N$: The First Stage / 3.1：
Construction of Wavelets on $bZ_N$: The Iteration Step / 3.2：
Examples and Applications / 3.3：
Wavelets on $bZ$ / 4：
$ ell ^2(bZ)$ / 4.1：
Complete Orthonormal Sets in Hilbert Spaces / 4.2：
$L^2([- pi , pi ))$ and Fourier Series / 4.3：
The Fourier Transform and Convolution on $ ell ^2(bZ)$ / 4.4：
First-Stage Wavelets on $bZ$ / 4.5：
The Iteration Step for Wavelets on $bZ$ / 4.6：
Implementation and Examples / 4.7：
Wavelets on $bR$ / 5：
$L^2(bR)$ and Approximate Identities / 5.1：
The Fourier Transform on $bR$ / 5.2：
Multiresolution Analysis and Wavelets / 5.3：
Construction of Multiresolution Analyses / 5.4：
Wavelets with Compact Support and Their Computation / 5.5：
Wavelets and Differential Equations / 6：
The Condition Number of a Matrix / 6.1：
Finite Difference Methods for Differential Equations / 6.2：
Wavelet-Galerkin Methods for Differential Equations / 6.3：
Bibliography
Index
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
30.

図書

東工大
目次DB
図書
東工大
目次DB
30. これなら分かる応用数学教室 : 最小二乗法からウェーブレットまで
金谷健一著
出版情報: 東京 : 共立出版, 2003.6  v, 270p ; 22cm
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目次情報: 続きを見る
第1章　最小二乗法 1
   1.1　データの表現 1
   　1.1.1　直線の当てはめ 1
   　1.1.2　多項式の当てはめ 8
   　1.1.3　一般の関数による近似 13
   　1.1.4　選点直交関数系 16
   1.2　関数の表現 17
   　1.2.1　関数の最小二乗近似 17
   　1.2.2　直交関数系 19
   　1.2.3　重みつき最小二乗近似 19
   　1.2.4　重みつき直交関数系 22
   1.3　列ベクトルの表現 23
   　1.3.1　列ベクトルの最小二乗近似 23
   　1.3.2　列ベクトルの直交系 26
第2章　直交関数展開 31
   2.1　関数の近似 31
   　2.1.1　直交関数系 31
   　2.1.2　最小二乗近似 33
   　2.1.3　重みつき直交関数系 37
   　2.1.4　重みつき最小二乗近似 41
   　2.1.5　選点直交関数系 45
   　2.1.6　選点最小二乗近似 47
   2.2　計量空間 49
   　2.2.1　内積とノルム 49
   　2.2.2　直交展開 57
   　2.2.3　直交射影 59
   　2.2.4　直交基底 60
   　2.2.5　シュミットの直交化 64
第3章　フーリエ解析 73
   3.1　フーリエ級数 73
   3.2　複素数の指数関数 78
   3.3　フーリエ級数の複素表示 81
   3.4　フーリエ変換 83
   3.5　たたみこみ積分 92
   3.6　フィルター 95
   3.7　パワースペクトル 97
   3.8　自己相関関数 102
   3.9　サンプリング定理 106
第4章　離散フーリエ解析 113
   4.1　離散フーリエ変換 113
   4.2　周期関数のサンプリング定理 118
   4.3　たたみこみ和定理 120
   4.4　パワースペクトル 123
   4.5　自己相関係数 126
   4.6　1の原始N乗根による表現 129
   4.7　高速フーリエ変換 132
   4.8　離散コサイン変換 139
第5章　固有値問題と2次形式 143
   5.1　線形代数のまとめ 143
   　5.1.1　連立1次方程式と行列式 143
   　5.1.2　余因子展開と逆行列 146
   　5.1.3　線形結合，線形独立，ランク 153
   　5.1.4　固有値と固有ベクトル 157
   5.2　2次形式とその標準形 165
   　5.2.1　2次形式 165
   　5.2.2　転置行列 168
   　5.2.3　直交行列 171
   　5.2.4　対称行列の固有値と固有ベクトル 175
   　5.2.5　対称行列の対角化とスペクトル分解 177
   　5.2.6　2次形式の標準形 178
   　5.2.7　正値対称行列と正値2次形式 185
第6章　主軸変換とその応用 193
   6.1　主成分分析 193
   　6.1.1　主軸変換 193
   　6.1.2　主成分 203
   6.2　画像の表現 208
   　6.2.1　画像の展開 208
   　6.2.2　画像の基底 210
   　6.2.3　画像の固有空間 214
   6.3　特異値分解 219
   　6.3.1　計算の効率化 219
   　6.3.2　特異値分解 226
第7章　ウェーブレット解析 231
   7.1　信号の階層的近似 231
   7.2　多重解像度分解 234
   7.3　スケーリング関数 237
   7.4　ウェーブレット 240
   7.5　ウェーブレット変換 245
   7.6　下降サンプリングと上昇サンプリング 249
   7.7　一般のウェーブレット 252
おわりに 259
索引 263
第1章　最小二乗法 1
   1.1　データの表現 1
   　1.1.1　直線の当てはめ 1
31.

図書
図書
31. Geometry of curves ([pbk.])
John W. Rutter
出版情報: Boca Raton ; London : Chapman & Hall/CRC, c2000  xvii, 361 p. ; 24 cm
シリーズ名: Chapman and Hall mathematics series
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Introduction
Cartesian coordinates / 0.1：
Polar coordinates / 0.2：
The Argand diagram / 0.3：
Polar equations / 0.4：
Angles / 0.5：
Orthogonal and parallel vectors / 0.6：
Trigonometry / 0.7：
Lines, circles, and conics / 1：
Lines / 1.1：
The circle / 1.2：
Conics / 1.3：
The ellipse in canonical position / 1.4：
The hyperbola in canonical position / 1.5：
The parabola in canonical position / 1.6：
Classical geometric constructions of conics / 1.7：
Polar equation of a conic with a focus as pole / 1.8：
History and applications of conics / 1.9：
Conics: general position / 2：
Geometrical method for diagonalisation / 2.1：
Algebra / 2.2：
Algebraic method for diagonalisation / 2.3：
Translating to canonical form / 2.4：
Central conics referred to their centre / 2.5：
Practical procedures for dealing with the general conic / 2.6：
Rational parametrisations of conics / 2.7：
Some higher curves / 3：
The semicubical parabola: a cuspidal cubic / 3.1：
A crunodal cubic / 3.2：
An acnodal cubic / 3.3：
A cubic with two parts / 3.4：
History and applications of algebraic curves / 3.5：
A tachnodal quartic curve / 3.6：
Limacons / 3.7：
Equi-angular (logarithmic) spiral / 3.8：
Archimedean spiral / 3.9：
Application - Watt's curves / 3.10：
Parameters, tangents, normal / 4：
Parametric curves / 4.1：
Tangents and normals at regular points / 4.2：
Non-singular points of algebraic curves / 4.3：
Parametrisation of algebraic curves / 4.4：
Tangents and normals at non-singular points / 4.5：
Arc-length parametrisation / 4.6：
Some results in analysis / 4.7：
Contact, inflexions, undulations / 5：
Contact / 5.1：
Invariance of point-contact order / 5.2：
Inflexions and undulations / 5.3：
Geometrical interpretation of n-point contact / 5.4：
An analytical interpretation of contact / 5.5：
Cusps, non-regular points / 6：
Cusps / 6.1：
Tangents at cusps / 6.2：
Contact between a line and a curve at a cusp / 6.3：
Higher singularities / 6.4：
Curvature / 7：
Curves given by polar equation / 7.1：
Curves in the Argand diagram / 7.3：
An alternative formula / 7.4：
Curvature: applications / 8：
Inflexions of parametric curves at regular points / 8.1：
Vertices and undulations at regular points / 8.2：
Curvature of algebraic curves / 8.3：
Limiting curvature of algebraic curves at cusps / 8.4：
Circle of curvature / 9：
Centre of curvature and circle of curvature / 9.1：
Contact between curves and circles / 9.2：
The equation / 10：
Non-regular points / 10.2：
Inflexions / 10.4：
Vertices / 10.5：
Undulations / 10.6：
The five classes of limacons / 10.7：
An alternative equation / 10.8：
Evolutes / 11：
Definition and special points / 11.1：
A matrix method for calculating evolutes / 11.2：
Evolutes of the cycloid and the cardioid / 11.3：
Parallels, involutes / 12：
Parallels of a curve / 12.1：
Involutes / 12.2：
Roulettes / 13：
General roulettes / 13.1：
Parametrisation of circles / 13.2：
Cycloids: rolling a circle on a line / 13.3：
Trochoids: rolling a circle on or in a circle / 13.4：
Rigid motions / 13.5：
Non-regular points and inflexions of roulettes / 13.6：
Envelopes / 14：
Evolutes as a model / 14.1：
Singular-set envelopes / 14.2：
Discriminant envelopes / 14.3：
Different definitions and singularities of envelopes / 14.4：
Limiting-position envelopes / 14.5：
Orthotomics and caustics / 14.6：
The relation between orthotomics and caustics / 14.7：
Orthotomics of a circle / 14.8：
Caustics of a circle / 14.9：
Singular points of algebraic curves / 15：
Intersection multiplicity with a given line / 15.1：
Homogeneous polynomials / 15.2：
Multiplicity of a point / 15.3：
Singular lines at the origin / 15.4：
Isolated singular points / 15.5：
Tangents and branches at non-isolated singular points / 15.6：
Branches for non-repeated linear factors / 15.7：
Branches for repeated linear factors / 15.8：
Cubic curves / 15.9：
Curvature at singular points / 15.10：
Projective curves / 16：
The projective line / 16.1：
The projective plane / 16.2：
The projective curve determined by a plane curve / 16.3：
Affine views of a projective curve / 16.5：
Plane curves as views of a projective curve / 16.6：
Tangent lines to projective curves / 16.7：
Boundedness of the associated affine curve / 16.8：
Summary of the analytic viewpoint / 16.9：
Asymptotes / 16.10：
Singular points and inflexions of projective curves / 16.11：
Equivalence of curves / 16.12：
Examples of asymptotic behaviour / 16.13：
Worked example / 16.14：
Practical work / 17：
Drawn curves / 18：
Personalising MATLAB for metric printing / 18.1：
Ellipse 1 and Ellipse 2 / 18.2：
Ellipse 3 / 18.3：
Parabola 1 / 18.4：
Parabola 2 / 18.5：
Parabola 3 / 18.6：
Hyperbola / 18.7：
Semicubical parabola / 18.8：
Polar graph paper / 18.9：
Further reading / 19：
Index
Introduction
Cartesian coordinates / 0.1：
Polar coordinates / 0.2：
32.

図書
図書
32. Problems and solutions in theoretical and mathematical physics (v. 1 Introductory level - v. 2 Advanced level : pbk)
Willi-Hans Steeb
出版情報: Singapore : World Scientific, c1996  2 v. ; 23 cm
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33.

図書
図書
33. A course of mathematical analysis (pt. 1 ; pt. 2)
A.F. Bermant ; translated by D.E. Brown ; translation edited by Ian N. Sneddon
出版情報: Oxford : Pergamon Press, 1963  2 v. ; 22 cm
シリーズ名: International series of monographs on pure and applied mathematics ; v. 30, 44
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34.

図書
図書
34. Derivation and integration
Washek F. Pfeffer
出版情報: Cambridge : Cambridge University Press, 2001  xvi, 266 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 140
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Preface
Acknowledgements
Preliminaries / 1.：
The setting / 1.1.：
Topology / 1.2.：
Measures / 1.3.：
Covering theorems / 1.4.：
Densities / 1.5.：
Lipschitz maps / 1.6.：
BV functions / 1.7.：
BV sets / 1.8.：
Slices of BV sets / 1.9.：
Approximating BV sets / 1.10.：
Charges / 2.：
The definition and examples / 2.1.：
Spaces of charges / 2.2.：
Derivates / 2.3.：
Derivability / 2.4.：
Reduced charges / 2.5.：
Partitions / 2.6：
Variations of charges / 3.：
Some classical concepts / 3.1.：
The essential variation / 3.2.：
The integration problem / 3.3.：
An excursion to Hausdorff measures / 3.4.：
The critical variation / 3.5.：
AC[subscript *] charges / 3.6.：
Essentially clopen sets / 3.7.：
Charges and BV functions / 4.：
The charge F x L[superscript 1] / 4.1.：
The space (CH[subscript *](E),S) / 4.2.：
Duality / 4.3.：
More on BV functions / 4.4.：
The charge F [angle] g / 4.5.：
Lipeomorphisms / 4.6.：
Integration / 5.：
The R-integral / 5.1.：
Multipliers / 5.2.：
Change of variables / 5.3.：
Averaging / 5.4.：
The Riemann approach / 5.5.：
Charges as distributional derivatives / 5.6.：
The Lebesgue integral / 5.7.：
Extending the integral / 6.：
Buczolich's example / 6.1.：
I-convergence / 6.2.：
The GR-integral / 6.3.：
Additional properties / 6.4.：
Bibliography
List of symbols
Index
Preface
Acknowledgements
Preliminaries / 1.：
35.

図書
図書
35. Practical quantum mechanics (v. 1 : gw - v. 2 : us)
Siegfried Flügge
出版情報: Berlin ; New York : Springer-Verlag, 1971  2 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 177-178
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36.

図書
図書
36. Analyse mathématique : cours professé à l'École polytechnique, Paris (1 ; 2)
Laurent Schwartz
出版情報: Paris : Hermann, c1967  2 v. ; 27 cm
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37.

図書
図書
37. Group theory (v. 1 : gw - v. 2 : pbk)
Michio Suzuki
出版情報: Berlin ; New York ; Tokyo : Springer-Verlag, c1982-c1986  2 v. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 247-248
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38.

図書
図書
38. Geometry of algebraic curves (v. 1 : us ; v. 1 : gw ; v. 2 : gw)
E. Arbarello ... [et al.]
出版情報: New York ; Tokyo : Springer-Verlag, c1985-c2011  2 v. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 267-268
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39.

図書
図書
39. Anwendungen der Laplace-Transformation (Abt. 1 ; Abt. 2)
von Gustav Doetsch
出版情報: Basel : Birkhäuser, 1955-1956  2 v. ; 25 cm
シリーズ名: Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften ; Mathematische Reihe ; Bd. 15,19 . Handbuch der Laplace-Transformation ; Bd. 2-3
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40.

図書
図書
40. 実験計画法講義 (1 : 基礎編(1) ; 2 : 基礎編(2))
北川敏男著
出版情報: 東京 : 培風館, 1955.11-1956.2  2冊 ; 22cm
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41.

図書
図書
41. 2次形式 (1 ; 2)
田坂隆士著
出版情報: 東京 : 岩波書店, 1976  2冊 (242p) ; 22cm
シリーズ名: 岩波講座基礎数学 / 小平邦彦監修 ; 岩堀長慶 [ほか] 編 ; 3 . 線型代数||センケイ ダイスウ ; 3
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42.

図書
図書
42. Superstring theory and beyond
Joseph Polchinski
出版情報: Cambridge ; New York : Cambridge University Press, 1998  xix, 531 p. ; 26 cm
シリーズ名: Cambridge monographs on mathematical physics ; . String theory / Joseph Polchinski ; v. 2
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目次情報: 続きを見る
Foreword
Preface
Notation
Type I and type II superstrings / 10：
The superconformal algebra / 10.1：
Ramond and Neveu-Schwarz sectors / 10.2：
Vertex operators and bosonization / 10.3：
The superconformal ghosts / 10.4：
Physical states / 10.5：
Superstring theories in ten dimensions / 10.6：
Modular invariance / 10.7：
Divergences of type I theory / 10.8：
Exercises
The heterotic string / 11：
World-sheet supersymmetries / 11.1：
The SO(32) and E[subscript 8] x E[subscript 8] heterotic strings / 11.2：
Other ten-dimensional heterotic strings / 11.3：
A little Lie algebra / 11.4：
Current algebras / 11.5：
The bosonic construction and toroidal compactification / 11.6：
Superstring interactions / 12：
Low energy supergravity / 12.1：
Anomalies / 12.2：
Superspace and superfields / 12.3：
Tree-level amplitudes / 12.4：
General amplitudes / 12.5：
One-loop amplitudes / 12.6：
D-branes / 13：
T-duality of type II strings / 13.1：
T-duality of type I strings / 13.2：
The D-brane charge and action / 13.3：
D-brane interactions: statics / 13.4：
D-brane interactions: dynamics / 13.5：
D-brane interactions: bound states / 13.6：
Strings at strong coupling / 14：
Type IIB string and SL(2,Z) duality / 14.1：
U-duality / 14.2：
SO(32) type I-heterotic duality / 14.3：
Type IIA string and M-theory / 14.4：
The E[subscript 8] x E[subscript 8] heterotic string / 14.5：
What is string theory? / 14.6：
Is M for matrix? / 14.7：
Black hole quantum mechanics / 14.8：
Advanced CFT / 15：
Representations of the Virasoro algebra / 15.1：
The conformal bootstrap / 15.2：
Minimal models / 15.3：
Coset models / 15.4：
Representations of the N = 1 superconformal algebra / 15.6：
Rational CFT / 15.7：
Renormalization group flows / 15.8：
Statistical mechanics / 15.9：
Orbifolds / 16：
Orbifolds of the heterotic string / 16.1：
Spacetime supersymmetry / 16.2：
Examples / 16.3：
Low energy field theory / 16.4：
Calabi-Yau compactification / 17：
Conditions for N = 1 supersymmetry / 17.1：
Calabi-Yau manifolds / 17.2：
Massless spectrum / 17.3：
Higher corrections / 17.4：
Generalizations / 17.6：
Physics in four dimensions / 18：
Continuous and discrete symmetries / 18.1：
Gauge symmetries / 18.2：
Mass scales / 18.3：
More on unification / 18.4：
Conditions for spacetime supersymmetry / 18.5：
Low energy actions / 18.6：
Supersymmetry breaking in perturbation theory / 18.7：
Supersymmetry beyond perturbation theory / 18.8：
Advanced topics / 19：
The N = 2 superconformal algebra / 19.1：
Type II strings on Calabi-Yau manifolds / 19.2：
Heterotic string theories with (2,2) SCFT / 19.3：
N = 2 minimal models / 19.4：
Gepner models / 19.5：
Mirror symmetry and applications / 19.6：
The conifold / 19.7：
String theories on K3 / 19.8：
String duality below ten dimensions / 19.9：
Conclusion / 19.10：
Spinors and SUSY in various dimensions / Appendix B：
Spinors in various dimensions / B.1：
Introduction to supersymmetry: d = 4 / B.2：
Supersymmetry in d = 2 / B.3：
Differential forms and generalized gauge fields / B.4：
Thirty-two supersymmetries / B.5：
Sixteen supersymmetries / B.6：
Eight supersymmetries / B.7：
References
Glossary
Index
Foreword
Preface
Notation
43.

図書
図書
43. An introduction to the bosonic string
Joseph Polchinski
出版情報: Cambridge ; New York : Cambridge University Press, 1998  xix, 402 p. ; 26 cm
シリーズ名: Cambridge monographs on mathematical physics ; . String theory / Joseph Polchinski ; v. 1
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Foreword
Preface
Notation
A first look at strings / 1：
Why strings? / 1.1：
Action principles / 1.2：
The open string spectrum / 1.3：
Closed and unoriented strings / 1.4：
Exercises
Conformal field theory / 2：
Massless scalars in two dimensions / 2.1：
The operator product expansion / 2.2：
Ward identities and Noether's theorem / 2.3：
Conformal invariance / 2.4：
Free CFTs / 2.5：
The Virasoro algebra / 2.6：
Mode expansions / 2.7：
Vertex operators / 2.8：
More on states and operators / 2.9：
The Polyakov path integral / 3：
Sums over world-sheets / 3.1：
Gauge fixing / 3.2：
The Weyl anomaly / 3.4：
Scattering amplitudes / 3.5：
Strings in curved spacetime / 3.6：
The string spectrum / 4：
Old covariant quantization / 4.1：
BRST quantization / 4.2：
BRST quantization of the string / 4.3：
The no-ghost theorem / 4.4：
The string S-matrix / 5：
The circle and the torus / 5.1：
Moduli and Riemann surfaces / 5.2：
The measure for moduli / 5.3：
More about the measure / 5.4：
Exercise
Tree-level amplitudes / 6：
Riemann surfaces / 6.1：
Scalar expectation values / 6.2：
The bc CFT / 6.3：
The Veneziano amplitude / 6.4：
Chan-Paton factors and gauge interactions / 6.5：
Closed string tree amplitudes / 6.6：
General results / 6.7：
One-loop amplitudes / 7：
CFT on the torus / 7.1：
The torus amplitude / 7.3：
Open and unoriented one-loop graphs / 7.4：
Toroidal compactification and T-duality / 8：
Toroidal compactification in field theory / 8.1：
Toroidal compactification in CFT / 8.2：
Closed strings and T-duality / 8.3：
Compactification of several dimensions / 8.4：
Orbifolds / 8.5：
Open strings / 8.6：
D-branes / 8.7：
T-duality of unoriented theories / 8.8：
Higher order amplitudes / 9：
General tree-level amplitudes / 9.1：
Higer genus Riemann surfaces / 9.2：
Sewing and cutting world-sheets / 9.3：
Sewing and cutting CFTs / 9.4：
General amplitudes / 9.5：
String field theory / 9.6：
Large order behavior / 9.7：
High energy and high temperature / 9.8：
Low dimensions and noncritical strings / 9.9：
A short course on path integrals / Appendix A：
Bosonic fields / A.1：
Fermionic fields / A.2：
References
Glossary
Index
Foreword
Preface
Notation
44.

図書
図書
44. ゲージ場の量子論 (1 ; 2)
九後汰一郎著
出版情報: 東京 : 培風館, 1989.7  2冊 ; 22cm
シリーズ名: 新物理学シリーズ / 山内恭彦監修 ; 23-24
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45.

図書
図書
45. Selecta (Vol. 1 : us - : set : sz)
Kurt Otto Friedrichs ; Cathleen S. Morawetz, editor
出版情報: Boston ; Basel : Birkhäuser, 1986  2 v. ; 26 cm
シリーズ名: Contemporary mathematicians
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46.

図書
図書
46. Introduction to toric varieties (: pbk)
by William Fulton
出版情報: Princeton, N.J. : Princeton University Press, 1993  xi, 157 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 131
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Definitions and examples / Ch. 1：
Introduction / 1.1：
Convex polyhedral cones / 1.2：
Affine toric varieties / 1.3：
Fans and toric varieties / 1.4：
Toric varieties from polytopes / 1.5：
Singularities and compactness / Ch. 2：
Local properties of toric varieties / 2.1：
Surfaces; quotient singularities / 2.2：
One-parameter subgroups; limit points / 2.3：
Compactness and properness / 2.4：
Nonsingular surfaces / 2.5：
Resolution of singularities / 2.6：
Orbits, topology, and line bundles / Ch. 3：
Orbits / 3.1：
Fundamental groups and Euler characteristics / 3.2：
Divisors / 3.3：
Line bundles / 3.4：
Cohomology of line bundles / 3.5：
Moment maps and the tangent bundle / Ch. 4：
The manifold with singular corners / 4.1：
Moment map / 4.2：
Differentials and the tangent bundle / 4.3：
Serre duality / 4.4：
Betti numbers / 4.5：
Intersection theory / Ch. 5：
Chow groups / 5.1：
Cohomology of nonsingular toric varieties / 5.2：
Riemann-Roch theorem / 5.3：
Mixed volumes / 5.4：
Bezout theorem / 5.5：
Stanley's theorem / 5.6：
Notes
References
Index of Notation
Index
Definitions and examples / Ch. 1：
Introduction / 1.1：
Convex polyhedral cones / 1.2：
47.

図書
図書
47. Concise complex analysis
Sheng Gong
出版情報: Singapore : World Scientific, c2001  xx, 176 p. ; 23 cm
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Preface
Foreward
Calculus / Chapter I：
A glimpse of calculus / 1.1：
Complex number field, extended complex plane and spherical representation / 1.2：
Complex differentiation / 1.3：
Complex integration / 1.4：
Elementary functions / 1.5：
Complex series / 1.6：
Exercises I
Cauchy integral theorem and Cauchy integral formula / Chapter II：
Cauchy-Green formula (Pompeiu formula) / 2.1：
Cauchy-Goursat theorem / 2.2：
Taylor series and Liouville theorem / 2.3：
Some results on zero points / 2.4：
Maximum modulus principle, Schwarz lemma, group of holomorphic automorphism / 2.5：
Integral representation of holomorphic function / 2.6：
Exercises II
Partition of unity / Appendix：
Theory of series of Weierstrass / Chapter III：
Laurent series / 3.1：
Isolate singularity / 3.2：
Entire functions and meromorphic functions / 3.3：
Weierstrass factorization theorem, Mittag-Leffler theorem and interpolation theorem / 3.4：
Residue theorem / 3.5：
Analytic continuation / 3.6：
Exercises III
Riemann mapping theorem / Chapter IV：
Conformal mapping / 4.1：
Normal family / 4.2：
Symmetric principle / 4.3：
Examples of Riemann surface / 4.5：
Schwarz-Christoffel formula / 4.6：
Exercises IV
Riemann surface
Differential geometry and Picard theorem / Chapter V：
Metric and curvature / 5.1：
Ahlfors-Schwarz lemma / 5.2：
Extension of Liouville theorem and value distribution / 5.3：
Picard little theorem / 5.4：
Extension of normal family / 5.5：
Picard great theorem / 5.6：
Exercises V
Curvature
Elementary facts on several complex variables / Chapter VI：
Introduction / 6.1：
Cartan theorem / 6.2：
Groups of holomorphic automorphisms of unit ball and unit bidisk / 6.3：
Poincare theorem / 6.4：
Hartogs theorem / 6.5：
References
Preface
Foreward
Calculus / Chapter I：
48.

図書
図書
48. Quantum fields and strings : a course for mathematicians (: set ; v. 1 ; v. 2)
Pierre Deligne ... [et al.], editors
出版情報: Providence, R.I. : American Mathematical Society, c1999  2 v. (xxii, 1501 p.) ; 27 cm
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Classical Fields and Supersymmetry: Notes on supersymmetry (following Joseph Bernstein) / P. Deligne ; J. W. MorganVolume 1, Part 1：
Notes on spinors
Classical field theory / D. S. Freed
Supersolutions
Sign manifesto
Formal Aspects of QFT: Note on quantization / Volume 1, Part 2：
Introduction to QFT / D. Kazhdan
Perturbative quantum field theory / E. Witten
Index of Dirac operators
Elementary Introduction to quantum field theory / L. Faddeev
Renormalization groups / D. Gross
Note on dimensional regularization / P. Etingof
Homework
Index
Conformal Field Theory and Strings: Lectures on conformal field theory / K. GawedzkiVolume 2, Part 3：
Perturbative string theory / E. D'Hoker
Super space descriptions of super gravity
Notes on 2d conformal field theory and string theory / D. Gaitsgory
Kaluza-Klein compactifications, supersymmetry, and Calabi-Yau spaces / A. Strominger
Dynamical Aspects of QFT: Dynamics of Quantum Field Theory / Volume 2, Part 4：
$N = 1$ supersymmetric field theories in four dimensions / N. Sieberg
Classical Fields and Supersymmetry: Notes on supersymmetry (following Joseph Bernstein) / P. Deligne ; J. W. MorganVolume 1, Part 1：
Notes on spinors
Classical field theory / D. S. Freed
49.

図書
図書
49. Harmonic analysis on semi-simple Lie groups (v. 1 : gw - v. 2 : pbk)
Garth Warner
出版情報: Berlin ; New York : Springer-Verlag, 1972  2 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 188-189
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50.

図書
図書
50. Nonlinear processes
[by] Richard Bellman
出版情報: New York : Academic Press, 1971  xix, 306 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v.40 . Introduction to the mathematical theory of control processes ; v. 2
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