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1.

図書

図書
Ioannis P. Stavroulakis, Stepan A. Tersian
出版情報: Singapore ; River Edge, N.J. : World Scientific, c1999  x, 297 p. ; 23 cm
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目次情報: 続きを見る
First-order Partial Differential Equations / 1.:
Introduction
Linear First-order Equations / 2.:
The Cauchy Problem for First-order Quasi-linear Equations / 3.:
General Solutions of Quasi-linear Equations / 4.:
Fully-nonlinear First-order Equations / 5.:
Second-order Partial Differential Equations
Linear equations / 6.:
Classification and Canonical Forms of Equations in Two Independent Variables / 7.:
Classification of Almost-linear Equations in R[superscript n] / 8.:
One-Dimensional Wave Equation
The Wave Equation on the Whole Line. D'Alembert Formula / 9.:
The Wave Equation on the Half-line. Reflection Method / 10.:
Mixed Problem for the Wave Equation / 11.:
Inhomogeneous Wave Equation / 12.:
Conservation of the Energy / 13.:
Weak Derivatives and Weak Solutions / 14.:
One-Dimensional Diffusion Equation
Maximum-minimum Principle for the Diffusion Equation / 15.:
The Diffusion Equation on the Whole Line / 16.:
Diffusion on the Half-line / 17.:
Inhomogeneous Diffusion Equation on the Whole Line / 18.:
Shock Waves and Conservation Laws
Conservation laws / 19.:
Burgers' Equation / 20.:
Weak Solutions. Riemann Problem / 21.:
Discontinuous Solutions of Conservation Laws. Rankine-Hugoniot Condition / 22.:
The Laplace Equation
Harmonic functions. Maximum-minimum Principle / 23.:
Green's Identities / 24.:
Green's Functions / 25.:
Green's Functions for a Half-space and Sphere / 26.:
Harnack's Inequalities and Theorems / 27.:
Fourier Series and Fourier Method for PDEs
Fourier Series / 28.:
Orthonormal Systems. General Fourier series / 29.:
Fourier Method for the Diffusion Equation / 30.:
Fourier Method for the Wave Equation / 31.:
Fourier Method for the Laplace Equation / 32.:
Diffusion and Wave Equations in Higher Dimensions
Diffusion Equation in Three Dimensional Space / 33.:
Fourier Method for the Diffusion Equation in Higher Dimensions / 34.:
Kirchoff's Formula for the Wave Equation. Huygens' Principle / 35.:
Fourier Method for the Wave Equation on the Plane. Nodal Sets / 36.:
References
Answers and Hints to Selected Exercises
Index
First-order Partial Differential Equations / 1.:
Introduction
Linear First-order Equations / 2.:
2.

図書

図書
by Zbigniew Haba
出版情報: Dordrecht : Kluwer Academic Publishers, c1999  xx, 364 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 480
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3.

図書

図書
Michael Monastyrsky ; with a foreword by Freeman J. Dyson ; translated by Roger Cooke, James King, Victoria King
出版情報: Boston : Birkhäuser, c1999  xiii, 215 p. ; 25 cm
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4.

図書

図書
edited by Alexander I. Bobenko and Ruedi Seiler
出版情報: New York : Oxford University Press, 1999  xxvii, 370 p. ; 25 cm
シリーズ名: Oxford lecture series in mathematics and its applications ; 16
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List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I:
Discretization of Surfaces and Integrable Systems / Ulrich Pinkall1:
A Discrete Version of the Darboux Transform for Isothermic Surfaces / Udo Hertrich-Jeromin ; Tim Hoffmann2:
Discrete Amsler Surfaces and a Discrete Painleve III Equation / 3:
Discrete cmc Surfaces and Discrete Holomorphic Maps / 4:
Discrete Indefinite Affine Spheres / Wolfgang K. Schief5:
Geometry of Discrete Curves and Lattices and Integrable Difference Equations / Adam Doliwa ; Paolo Maria Santini6:
Classical Systems / II:
R-matrices and Integrable Discretizations / Yuri B. Suris7:
Discrete Painleve Equations and Symmetry Reduction on the Lattice / Frank W. Nijhoff8:
Lagrangian Description of Doubly Discrete Sine-Gordon Type Models / Nadja Kutz9:
Quantum Systems / III:
Spectra of Quantum Integrals / Johannes Kellendonk10:
Algebraic Quantization of Integrable Models in Discrete Space-Time / Ludwig D. Faddeev ; Alexander Yu. Volkov11:
Affine Toda Field Theory as a Three-dimensional Integrable System / Rinat M. Kashaev ; Nikolai Yu. Reshetikhin12:
Quantum Hyperbolic Invariants of Knots / 13:
Charge Transport in the Discretized Landau Model / Thomas Richter14:
Index
List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I:
5.

図書

図書
by Uwe Franz and René Schott
出版情報: Dordrecht : Kluwer, c1999  vii, 227 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 490
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Preface
Introduction / 1:
Preliminaries on Lie groups / 2:
Hopf algebras, quantum groups and braided spaces / 3:
Stochastic Processes on quantum groups / 4:
Markov Structure of quantum Levy Processes / 5:
Diffusions on braided spaces / 6:
Evolution equations and Levy processes on quantum groups / 7:
Gauss Laws in the sense of Bernstein on quantum groups / 8:
Phase retrieval for probability distributions on quantum groups / 9:
Limit theorems on quantum groups / 10:
Bibliography
Index
Preface
Introduction / 1:
Preliminaries on Lie groups / 2:
6.

図書

図書
David A. Cox, Sheldon Katz
出版情報: Providence, R.I. : American Mathematical Society, c1999  xxi, 469 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 68
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Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
Hodge theory and Yukawa couplings
Moduli spaces Gromov-Witten invariants
Quantum cohomology Localization
Quantum differential equations
The mirror theorem Conclusion
Singular varieties
Physical theories
Bibliography
Index
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
7.

図書

図書
edited by Silvio Levy
出版情報: Cambridge [England] : Cambridge University Press, 1999  x, 331 p., [4] p. of col. plates ; 25 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 35
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8.

図書

図書
Erwin Kreyszig
出版情報: New York : John Wiley & Sons, c1999  xvi, 1156, 97, 20 p. ; 26-27 cm
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目次情報: 続きを見る
How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A:
First-Order ODEs / Chapter 1:
Second-Order Linear ODEs / Chapter 2:
Ordinary Differential Equations (Ode's)
First-Order ODE's / Chapter 3:
Higher Order Linear ODEs
Second Order Linear ODE's / Chapter 4:
Systems of ODEs. Phase Plane. Qualitative Methods
Higher Order Linear ODE's
Systems of ODE's Phase Plane, Qualitative Methods / Chapter 5:
Series Solutions of ODEs. Special Functions
Series Solutions of ODE's Special Functions / Chapter 6:
Laplace Transforms
Linear Algebra, Vector Calculus / Part B:
Linear Algebra: Matrices, Vectors, Determinants: Linear Systems / Chapter 7:
Matrices, Vectors, Determinants. Linear Systems / Chapter 8:
Linear Algebra: Matrix Eigenvalue Problems
Vector Differential Calculus: Grad, Div, Curl / Chapter 9:
Vector Integral Calculus: Integral Theorems / Chapter 10:
Vector Differential Calculus. Grad, Div, Curl / Part C:
Fourier Analysis, Partial Differential Equations
Fourier Series, Integrals, and Transforms / Chapter 11:
Vector Integral Calculus. Integral Theorems
Partial Differential Equations (PDE 's) / Chapter 12:
Fourier Analysis. Partial Differential Equations / Chapter 13:
Complex Numbers and Functions
Complex Integration / Chapter 14:
Power Series, Taylor Series / Chapter 15:
Partial Differential Equations (PDEs) / Chapter 16:
Laurent Series: Residue Integration
Conformal Mapping / Part D:
Complex Analysis
Complex Analysis and Potential Theory / Chapter 18:
Numerical Analysis Software / Part E:
Numerics in General / Chapter 19:
Numerical Linear Algebra / Chapter 20:
Numerics for ODE 's and PDE 's / Chapter 21:
Optimization, Graphs / Part F:
Laurent Series. Residue Integration
Unconstrained Optimization: Linear Programming / Chapter 22:
Graphs, Combinatorial Optimization / Chapter 23:
Probability / Part G:
Statistics
Data Analysis / Chapter 24:
Numeric Analysis
Probability Theory
Mathematical Statistics / Chapter 25:
References / Appendix 1:
Numeric Linear Algebra / Appendix 2:
Answers to Odd-Numbered Problems
Auxiliary Material / Appendix 3:
Numerics for ODEs and PDEs
Additional Proofs / Appendix 4:
Tables / Appendix 5:
Index
Unconstrained Optimization. Linear Programming
Graphs and Combinatorial Optimization
Probability, Statistics
Data Analysis. Probability Theory
Photo Credits
How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A:
First-Order ODEs / Chapter 1:
9.

図書

図書
by Volodymyr Koshmanenko
出版情報: Dordrecht ; Boston : Kluwer, 1999  viii, 308 p.
シリーズ名: Mathematics and its applications ; v. 474
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Preface to the English Edition
Introduction
Quadratic Forms and Linear Operators / 1:
Singular Quadratic Forms / 2:
Singular Perturbations of Self-Adjoint Operators / 3:
Applications to Quantum Field Theory / 4:
References
Subject Index
Notation
Preface to the English Edition
Introduction
Quadratic Forms and Linear Operators / 1:
10.

図書

図書
David E. Evans and Yasuyuki Kawahigashi
出版情報: Oxford : Clarendon Press, 1998  xv, 829 p. ; 24 cm
シリーズ名: Oxford mathematical monographs
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