1.
図書
谷山豊著 ; 杉浦光夫 [ほか] 編
出版情報:
東京 : 日本評論社, 1994.10 369p, 図版 [1] 枚 ; 27cm
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Jacobian varieties and number fields : a mimeographed note, University of Tokyo (September, 1955)
Jacobian varieties and number fields : mimeographed notes (the International Symposium on Algebraic Number Theory, Tokyo-Nikko, September, 1955)
Jacobian varieties and number fields : proceedings of the International Symposium on Algebraic Number Theory, Tokyo-Nikko, 1955; pp.31-45; (October, 1956)
On a certain relation between L-functions : an unpublished manuscript dated February 4, 1956
Regular local system for an abelian extension : an unpublished manuscript written on February 17, 1956
A letter to André Weil
L-functions of number fields and zeta functions of abelian varieties : Journal of the Mathematical Society of Japan, vol.9, pp.330-366 (July, 1957)
Distribution of positive 0-cycles in absolute classes of an algebraic variety with finite constant field : Scientific papers of the College of General Education, University of Tokyo, Vol.8, pp.123-137 (1958)
Problems
ABEL函数体ノn-分割ニツイテ : WEILノ有限性定理ノ代数的証明
日本数学会講演アブストラクト
Jacobi多様体と数体
虚数乗法に関する非公式討論会
問題
A.Weilの印象
A.Weilをめぐって
類体の構成について
モヅル函数と合同ζ-函数
整数論
空々しさということ
虚数乗法と合同ζ-函数
シンポジウムについて
代数幾何学と整数論
A.Weilに接して
Weylと整数論
数論グループ
代数的整数論におけるζ-函数
巻頭に寄せて
少数精鋭主義について
整数論展望
数理科学研究所設立の問題について : 全国の研究者各位に訴える
米国留学について二つの意見
大学院の問題について
応用数学小委員会への質問状 : 数理研の問題について
ヒルベルトのモヂュラー函数について
(自己紹介)
「零 (ゼロ) の発見」
「科学と方法」
1955年国際数学会議
Quelques questions
或る映画を見てある人がどう考へるかと云ふことについて : 一つの実例
四行詩
屋上屋を架す
正雄さんの話
正夫さんの話
現代数学の性格について
新人紹介 Peter Roquette
A.Weil「ゼータ函数の育成について」
A.Weil「イデール類群の或る指標について」
『近代的整数論』第1章歴史
Jacobian varieties and number fields : a mimeographed note, University of Tokyo (September, 1955)
Jacobian varieties and number fields : mimeographed notes (the International Symposium on Algebraic Number Theory, Tokyo-Nikko, September, 1955)
Jacobian varieties and number fields : proceedings of the International Symposium on Algebraic Number Theory, Tokyo-Nikko, 1955; pp.31-45; (October, 1956)
2.
図書
Michael Frame and Benoit B. Mandelbrot, editors ; foreword by Lynn Arthur Steen
出版情報:
[Washington, D.C.] : Mathematical Association of America, c2002 xiii, 206 p., [4] p. of plates ; 28 cm
シリーズ名:
MAA notes ; 58
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Foreword / Lynn Arthur Steen
Preface
Introductory Essays
Some Reasons for the Effectiveness of Fractals in Mathematics Education / Benoit B. Mandelbrot ; Michael Frame1.：
Unsolved Problems and Still-Emerging Concepts in Fractal Geometry / 2.：
Fractals, Graphics, and Mathematics Education / 3.：
Mathematics and Society in the 20th Century / 4.：
Classroom Experiences
Teaching Fractals and Dynamical Systems at The Hotchkiss School / Melkana Brakalova ; David Coughlin5.：
Reflecting on Wada Basins: Some Fractals with a Twist / Dane Camp6.：
Learning and Teaching about Fractals / Donald M. Davis7.：
The Fractal Geometry of the Mandelbrot Set: Periods of the Bulbs / Robert L. Devaney8.：
Fractals--Energizing the Mathematics Classroom / Vicki Fegers ; Mary Beth Johnson9.：
Other Chaos Games / Sandy Fillebrown10.：
Creating and Teaching Undergraduate Courses and Seminars in Fractal Geometry: a Personal Experience / Michel Lapidus11.：
Exploring Fractal Dimensions by Experiment / Ron Lewis12.：
Fractal Themes at Every Level / Kenneth G. Monks13.：
Art and Fractals: Artistic Explorations of Natural Self-Similarity / Brianna Murratti14.：
Order and Chaos, Art and Magic: a First College Course in Quantitative Reasoning Based on Fractals and Chaos / David Peak15.：
A Software Driven Undergraduate Fractals Course / Douglas C. Ravenel16.：
A Final Word
The Fractal Ring from Art to Art through Mathematics, Finance, and the Sciences / 17.：
Appendices
Panorama of Fractals and Their Uses. An Alphabetic Wordbook-Index / 18.：
Reports of Some Field Experiences / 19.：
Guide to Topics
References
About the Editors and Other Contributors
Index
Foreword / Lynn Arthur Steen
Preface
Introductory Essays
3.
図書
Dietrich Braess ; translated by Larry L. Schumaker
出版情報:
Cambridge : Cambridge University Press, 2001 xvii, 352 p. ; 23 cm
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Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
Notation
Introduction / Chapter I：
Examples and Classification of PDE's / 1：
Examples
Classification of PDE's
Well-posed Problems
Problems
The Maximum Principle / 2：
Corollaries
Problem
Finite Difference Methods / 3：
Discretization
Discrete maximum principle
A Convergence Theory for Difference Methods / 4：
Consistency
Local and global error
Limits of the convergence theory
Conforming Finite Elements / Chapter II：
Sobolev Spaces
Introduction to Sobolev spaces
Friedrichs' inequality
Possible singularities of H1 functions
Compact imbeddings
Variational Formulation of Elliptic Boundary-Value Problems of Second Order
Variational formulation
Reduction to homogeneous boundary conditions
Existence of solutions
Inhomogeneous boundary conditions
The Neumann Boundary-Value Problem. A Trace Theorem
Ellipticity in H1
Boundary-value problems with natural boundary conditions
Neumann boundary conditions
Mixed boundary conditions
Proof of the trace theorem
Practical consequences of the trace theorem
The Ritz-Galerkin Method and Some Finite Elements
Model Problem
Some Standard Finite Elements / 5：
Requirements on the meshes
Significance of the differentiability properties
Triangular elements with complete polynomials
Remarks on C1 elements
Bilinear elements
Quadratic rectangular elements
Affine families
Choice of an element
Approximation Properties / 6：
The Bramble-Hilbert lemma
Bilinear quadrilateral elements
Inverse estimates
Clément's interpolation
Appendix: On the optimality of the estimates
Error Bounds for Elliptic Problems of Second Order / 7：
Remarks on regularity
Error bounds in the energy norm
L2 estimates
A simple L? estimate
The L2-projector
Computational Considerations / 8：
Assembling the stiffness matrix
Static condensation
Complexity of setting up the matrix
Effect on the choice of a grid
Local mesh refinement
Implementation of the Neumann boundary-value Problem
Nonconforming and Other Methods / Chapter III：
Abstract Lemmas and a Simple Boundary Approximation
Generalizations of Céa's lemma
Duality methods
The Crouzeix-Raviart element
A Simple approximation to curved boundaries
Modifications of the duality argument
Isoparametric Elements
Isoparametric triangular elements
Isoparametric quadrilateral elements
Further Tools from Functional Analysis
Negative norms
Adjoint operators
An abstract existence theorem
An abstract convergence theorem
Proof of Theorem 3.4
Saddle Point Problems
Saddle points and minima
The inf-sup condition
Mixed finite element methods
Fortin interpolation
Saddle point problems with penalty term
Typical applications
Mixed Methods for the Poisson Equation
The Poisson equation as a mixed problem
The Raviart - Thomas element
Interpolation by Raviart-Thomas elements
Implementation and postprocessing
Mesh-dependent norms for the Raviart-Thomas element
The Softening behaviour of mixed methods
The Stokes Equation
Nearly incompressible flows
Finite Elements for the Stokes Problems
An instable element
The Taylor-Hood element
The MINI element
The divergence-free nonconforming P1 element
A Posteriori Error Estimates
Residual estimators
Lower estimates
Remark on other estimators
Local mesh refinement and convergence
A Posteriori Error Estimates via the Hypercircle Method / 9：
The Conjugate Gradient Method / Chapter IV：
Classical Iterative Methods for Solving Linear Systems
Stationary linear processes
The Jacobi and Gauss-Seidel methods
The model problem
Overrelaxation
Gradient Methods
The general gradient method
Gradient methods and quadratic functions
Convergence behavior in the case of large condition numbers
Conjugate Gradient and the Minimal Residual Method
The CG algorithm
Analysis of the CG method as an optimal method
The minimal residual method
Indefinite and unsymmetric matrices
Preconditioning
Preconditioning by SSOR
Preconditioning by ILU
Remarks on parallelization
Nonlinear Problems
The Uzawa algorithm and its variants
An alternative
Multigrid Methods / Chapter V：
Multigrid Methods for Variational Problems
Smoothing properties of classical iterative methods
The multigrid idea
The algorithm
Transfer between grids
Convergence of Multigrid Methods
Discrete norms
Connection with the Sobolev norm
Approximation property
Convergence proof for the two-grid method
An alternative short proof
Some variants
Convergence for Several Levels
A recurrence formula for the W-cycle
An improvement for the energy norm
The convergence proof for the V-cycle
Nested Iteration
Computation of starting values
Complexity
Multigrid methods with a small number of levels
The CASCADE algorithm
Multigrid Analysis via Space Decomposition
Schwarz alternating method
Assumptions
Direct consequences
Convergence of multiplicative methods
Verification of A1
Local mesh refinements
The multigrid-Newton method
The nonlinear multigrid method
Starting values
Finite Elements in Solid Mechanics / Chapter VI：
Introduction to Elasticity Theory
Kinematics
The equilibrium equations
The Piola transform
Constitutive Equations
Linear material laws
Hyperelastic Materials
Linear Elasticity Theory
The variational problem
The displacement formulation
The mixed method of Hellinger and Reissner
The mixed method of Hu and Washizu
Nearly incompressible material
Locking
Locking of the Timoshenko beam and typical remedies
Membranes
Plane stress states
Plane strain states
Membrane elements
The PEERS element
Beams and Plates: The Kirchhoff Plate
The hypotheses
Note on beam models
Mixed methods for the Kirchoff plate
DKT elements
The Mindlin-Reissner Plate
The Helmholtz decomposition
The mixed formulation with the Helmholtz decomposition
MITC elements
The Model without a Helmboltz decomposition
References
Index
Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
4.
図書
Jack Hale
5.
図書
M.L. Mehta
出版情報:
New York : Academic Press, 1967 x, 259 p. ; 24 cm
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6.
図書
Shlomo Sternberg
7.
図書
Robert Gilmore
出版情報:
New York : Wiley, c1974 xx, 587 p. ; 23 cm
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8.
図書
N.N. Bogoliubov and Y.A. Mitropolsky
9.
図書
by Carl B. Boyer ; with a foreword by Richard Courant
10.
図書
edited by Eli Mishkin and Ludwig Braun, Jr. ; contributors, John G. Truxal ... [et al.]
11.
図書
by S. Chandrasekhar
12.
図書
Dimitris N. Chorafas
13.
図書
F. Calogero
14.
図書
Lamberto Cesari
15.
図書
by Thomas S. Ferguson
16.
図書
edited by Felix E. Browder
出版情報:
Berlin ; New York : Springer, 1970 241 p. ; 24 cm
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17.
図書
H.F. Bohnenblust ... [et al.] ; edited by H.W. Kuhn and A.W. Tucker
18.
図書
Wilhelm Klingenberg
19.
図書
Aubin Jean-Pierre
出版情報:
Paris : Gauthier-Villars, c1984 287 p. ; 25 cm
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20.
図書
edited by J. M. Mendel and K. S. Fu
21.
図書
Edward Angel, Richard Bellman
22.
図書
Rutherford Aris
23.
図書
C.H. Edwards, Jr
出版情報:
New York ; Heidelberg ; Berlin ; Tokyo : Springer-Verlag, c1979 xii, 351 p. ; 25 cm
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Area Number and Limit Concepts in Antiquity / 1：
Archimedes / 2：
Twilight, Darkness and Dawn / 3：
Early Indivisibles and Infinitesimal Techniques / 4：
Early Tangent Constructions / 5：
Napier's Wonderful Logarithms / 6：
The Arithmetic of the Infinite / 7：
The Calculus According to Newton / 8：
The Calculus According to Leibniz / 9：
The Age of Euler / 10：
The Calculus According to Cauchy, Riemann and Weierstrass / 11：
Postscript: The Twentieth Century / 12：
Index
Area Number and Limit Concepts in Antiquity / 1：
Archimedes / 2：
Twilight, Darkness and Dawn / 3：
24.
図書
J. Aczél, Z. Daróczy
25.
図書
[by] Arthur Albert
26.
図書
[by] Erik M. Alfsen
27.
図書
Karl J. Åström
目次情報:
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Preface
Contents
Overview / 1：
Methods of Operator Approximation in System Modelling / I：
Nonlinear Operator Approximation with Preassigned Accuracy / 2：
Introduction / 2.1：
Generic formulation of the problem / 2.2：
Operator approximation in space C([0; 1]) / 2.3：
Operator approximation in Banach spaces by polynomial operators / 2.4：
Approximation on compact sets in topological vector spaces / 2.5：
Approximation on noncompact sets in Hilbert spaces / 2.6：
Special results for maps into Banach spaces / 2.7：
Concluding remarks / 2.8：
Interpolation of Nonlinear Operators 65 / 3：
Lagrange interpolation in Banach spaces / 3.1：
Weak interpolation of nonlinear operators / 3.3：
Some related results / 3.4：
Realistic Operators and their Approximation / 3.5：
Formalization of concepts related to description of real-world objects / 4.1：
Approximation of RÂícontinuous operators / 4.3：
Methods of Best Approximation for Nonlinear Operators / 4.4：
Best Approximation of nonlinear operators in Banach spaces: Deterministic case / 5.1：
Estimation of mean and covariance matrix for random vectors / 5.3：
Best Hadamard-quadratic approximation / 5.4：
Best polynomial approximation / 5.5：
Best causal approximation / 5.6：
Best hybrid approximations / 5.7：
Optimal Estimation of Random Vectors / 5.8：
Computational Methods for Optimal Filtering of Stochastic Signals / 6：
Optimal linear Filtering in Finite dimensional vector spaces / 6.1：
Optimal linear Filtering in Hilbert spaces / 6.3：
Optimal causal linear Filtering with piecewise constant memory / 6.4：
Optimal causal polynomial Filtering with arbitrarily variable memory / 6.5：
Optimal nonlinear Filtering with no memory constraint / 6.6：
Computational Methods for Optimal Compression and Reconstruction of Random Data / 6.7：
Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) / 7.1：
Rank-constrained matrix approximations / 7.3：
Generic PCA{KLT / 7.4：
Optimal hybrid transform based on Hadamard-quadratic approximation / 7.5：
Optimal transform formed by a combination of nonlinear operators / 7.6：
Optimal generalized hybrid transform / 7.7：
Bibliography / 7.8：
Index
Preface
Contents
Overview / 1：
28.
図書
F.V. Atkinson
29.
図書
edited by A. Grasselli
出版情報:
New York : Academic Press, 1969 xi, 436 p. ; 24 cm
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30.
図書
[by] Paul B. Bailey, Lawrence F. Shampine [and] Paul E. Waltman
31.
図書
by Ranan B. Banerji
32.
図書
based, in part, on notes left by Harry Bateman ; and compiled by the staff of the Bateman Manuscript Project. [A Erdélyi, editor. W. Magnus, F. Oberhettinger, F.G. Tricomi, research associates]
出版情報:
New York : McGraw-Hill, 1954-1955 3 v ; 24 cm
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33.
図書
Anatole Beck ; with the assistance of Jonathan and Mirit Lewin
34.
図書
Christian Berg, Gunnar Forst
35.
図書
John Benedetto
36.
図書
by Austin Blaquière, Françoise Gérard [and] George Leitmann
37.
図書
by Armand Borel ; with contributions by G. Bredon ... [et al.]
38.
図書
James R. Brown
39.
図書
Robert F. Brown
出版情報:
Glenview, Ill. : Scott, Foresman, c1971 vi, 186 p. ; 24 cm
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40.
図書
[by] Garrett Birkhoff and Thomas C. Bartee
出版情報:
New York : McGraw-Hill, c1970 xi, 431 p. ; 23 cm
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41.
図書
[by] Stephen R. Bernfeld [and] V. Lakshmikantham
42.
図書
by Richard L. Bishop and Samuel I. Goldberg
出版情報:
New York : Macmillan, c1968 viii, 280 p. ; 24 cm
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43.
図書
By A.V. Bitsadze ; Translated from the Russian by Scripta Technica, ltd. ; Translation edited by M.J. Laird
44.
図書
S. Bosch, U. Güntzer, R. Remmert
45.
図書
by A.T. Bharucha-Reid
46.
図書
R. N. Bhattacharya, R. Ranga Rao
47.
図書
Gerald J. Bierman
48.
図書
[by] Umberto Bertelè and Francesco Brioschi
49.
図書
János Bognár
50.
図書
[by] F.F. Bonsall [and] J. Duncan
51.
図書
William M. Boothby
目次情報:
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Preface to the Revised Second Edition
Preface to the Second Edition
Preface to the First Edition
Introduction to Manifolds / I.：
Preliminary Comments on R[superscript n] / 1.：
R[superscript n] and Euclidean Space / 2.：
Topological Manifolds / 3.：
Further Examples of Manifolds. Cutting and Pasting / 4.：
Abstract Manifolds. Some Examples / 5.：
Functions of Several Variables and Mappings / II.：
Differentiability for Functions of Several Variables
Differentiability of Mappings and Jacobians
The Space of Tangent Vectors at a Point of R[superscript n]
Another Definition of T[subscript a](R[superscript n])
Vector Fields on Open Subsets of R[superscript n]
The Inverse Function Theorem / 6.：
The Rank of a Mapping / 7.：
Differentiable Manifolds and Submanifolds / III.：
The Definition of a Differentiable Manifold
Further Examples
Differentiable Functions and Mappings
Rank of a Mapping, Immersions
Submanifolds
Lie Groups
The Action of a Lie Group on a Manifold. Transformation Groups
The Action of a Discrete Group on a Manifold / 8.：
Covering Manifolds / 9.：
Vector Fields on a Manifold / IV.：
The Tangent Space at a Point of a Manifold
Vector Fields
One-Parameter and Local One-Parameter Groups Acting on a Manifold
The Existence Theorem for Ordinary Differential Equations
Some Examples of One-Parameter Groups Acting on a Manifold
One-Parameter Subgroups of Lie Groups
The Lie Algebra of Vector Fields on a Manifold
Frobenius's Theorem
Homogeneous Spaces
Tensors and Tensor Fields on Manifolds / V.：
Tangent Covectors
Covectors on Manifolds
Covector Fields and Mappings
Bilinear Forms. The Riemannian Metric
Riemannian Manifolds as Metric Spaces
Partitions of Unity
Some Applications of the Partition of Unity
Tensor Fields
Tensors on a Vector Space
Mappings and Covariant Tensors
The Symmetrizing and Alternating Transformations
Multiplication of Tensors
Multiplication of Tensors on a Vector Space
Multiplication of Tensor Fields
Exterior Multiplication of Alternating Tensors
The Exterior Algebra on Manifolds
Orientation of Manifolds and the Volume Element
Exterior Differentiation
An Application to Frobenius's Theorem
Integration on Manifolds / VI.：
Integration in R[superscript n] Domains of Integration
Basic Properties of the Riemann Integral
A Generalization to Manifolds
Integration on Riemannian Manifolds
Integration on Lie Groups
Manifolds with Boundary
Stokes's Theorem for Manifolds
Homotopy of Mappings. The Fundamental Group
Homotopy of Paths and Loops. The Fundamental Group
Some Applications of Differential Forms. The de Rham Groups
The Homotopy Operator
Some Further Applications of de Rham Groups
The de Rham Groups of Lie Groups
Covering Spaces and Fundamental Group
Differentiation on Riemannian Manifolds / VII.：
Differentiation of Vector Fields along Curves in R[superscript n]
The Geometry of Space Curves
Curvature of Plane Curves
Differentiation of Vector Fields on Submanifolds of R[superscript n]
Formulas for Covariant Derivatives
[down triangle, open subscript x subscript p] Y and Differentiation of Vector Fields
Constant Vector Fields and Parallel Displacement
Addenda to the Theory of Differentiation on a Manifold
The Curvature Tensor
The Riemannian Connection and Exterior Differential Forms
Geodesic Curves on Riemannian Manifolds
The Tangent Bundle and Exponential Mapping. Normal Coordinates
Some Further Properties of Geodesics
Symmetric Riemannian Manifolds
Some Examples
Curvature / VIII.：
The Geometry of Surfaces in E[superscript 3]
The Principal Curvatures at a Point of a Surface
The Gaussian and Mean Curvatures of a Surface
The Theorema Egregium of Gauss
Basic Properties of the Riemann Curvature Tensor
Curvature Forms and the Equations of Structure
Differentiation of Covariant Tensor Fields
Manifolds of Constant Curvature
Spaces of Positive Curvature
Spaces of Zero Curvature
Spaces of Constant Negative Curvature
References
Index
Preface to the Revised Second Edition
Preface to the Second Edition
Preface to the First Edition
52.
図書
[by] R. Boudarel, J. Delmas [and] P. Guichet ; translated by R.N. McDonough
53.
図書
Max D. Larsen, Paul J. McCarthy
54.
図書
Arthur A. Sagle, Ralph E. Walde
目次情報:
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Preface
Some Calculus / Chapter 1.：
Basic Notation / 1.：
The Derivative / 2.：
Higher Derivatives / 3.：
Taylor's Formula / 4.：
Inverse Function Theorem / 5.：
The Algebra gl(V) / 6.：
Manifolds / Chapter 2.：
Differentiable Structures
Differentiable Functions
Submanifolds
Tangents and Cotangents
Tangent Maps (Differentials)
Tangent Bundle
Vector Fields / 7.：
Integral Curves / 8.：
Topological Groups / Chapter 3.：
Basics
Subgroups and Homogeneous Spaces
Connected Groups
Lie Groups / Chapter 4.：
Basic Structures
Local Lie Groups
Lie Subgroups
The Lie Algebra of a Lie Group / Chapter 5.：
The Lie Algebra
The Exponential Map
Exponential Formulas
Homomorphisms and Analytic Structure
Lie Subgroups and Subalgebras / Chapter 6.：
Lie Subalgebra and Uniqueness of Analytic Structure
Local Isomorphisms
Closed Subgroups
Homogeneous Spaces
Commutative Lie Groups
Automorphisms and Adjoints / Chapter 7.：
Automorphisms of Algebras
Inner Derivations and Automorphisms
Adjoint Representations
Simply Connected Lie Groups / Chapter 8.：
Homotopy Review
Simply Connected Covering Groups
Some Algebra / Chapter 9.：
Tensor Products
Extension of the Base Field
Complexification
Modules and Representations
Semisimple Modules
Composition Algebras
Solvable Lie Groups and Algebras / Chapter 10.：
Solvable Lie Groups
Solvable Lie Algebras and Radicals
Lie's Theorem on Solvability
Nilpotent Lie Groups and Algebras / Chapter 11.：
Nilpotent Lie Groups
Nilpotent Lie Algebras
Nilpotent Lie Algebras of Endomorphisms
Semisimple Lie Groups and Algebras / Chapter 12.：
Invariant Bilinear Forms
Cartan's Criteria
Ideals and Derivations of Semisimple Lie Algebras
Complete Reducibility and Semisimplicity
More on Radicals, Derivations, and Tensor Products
Remarks on Real Simple Lie Algebras and Compactness
Cartan Subalgebras and Root Spaces / Chapter 13.：
Cartan Subalgebras
Root Spaces of Split Semisimple Lie Algebras
Irreducible Representations of sl(2,K)
Simple Split Lie Algebras / Chapter 14.：
Root Systems
Classification of Split Simple Lie Algebras
On Automorphisms of Simple Complex Lie Algebras
Simple Real Lie Algebras and Groups / Chapter 15.：
Real Forms of Simple Complex Lie Algebra
Representations of Real and Complex Simple Lie Algebras
Some Simple Real and Complex Lie Groups
Some Differential Geometry / Appendix.：
Connections on Manifolds
Connections on Homogeneous Spaces and Nonassociative Algebras
Multiplicative Systems and Connections
Riemannian Connections and Jordan Algebras
References
Index
Preface
Some Calculus / Chapter 1.：
Basic Notation / 1.：
55.
図書
Wilhelm Magnus
56.
図書
B.M. Puttaswamaiah, John D. Dixon
57.
図書
Grzegorz Rozenberg, Arto Salomaa
58.
図書
J.H. Wilkinson, C. Reinsch ; chief editor, F.L. Bauer
59.
図書
A. Hanyga ; translation editor, R.W. Ogden
60.
図書
Paul J. Kelly, Max L. Weiss
61.
図書
edited by A.V. Balakrishnan, Lucien W. Neustadt
出版情報:
New York : Academic Press, 1967 xv, 459 p. ; 24 cm
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62.
図書
edited by Garrett Birkhoff ; with the assistance of Uta Merzbach
目次情報:
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Foundations of Real Analysis / Part 1：
Cauchy's Partial Rigorization / A：
Cauchy on Limits and Continuity / 1a：
Cauchy on convergence / 1b：
Cauchy on the Radius of Convergence / 1c：
Cauchy on the Derivative as a Limit / 2：
Cauchy on Maclaurin's Theorem / 3：
Cauchy-Moigno on the Fundamental Theorem of the Calculus / 4：
Continuity and Integrability / B：
Bolzano on Continuity and Limits / 5：
Riemann on Fourier Series and the Riemann Integral / 6：
Heine Discusses Fourier Series / 7a：
Heine on the Foundations of Function Theory / 7b：
Stieltjes on the Stieltjes Integral / 8：
Foundations of Complex Analysis / Part 2：
Early Developments
Cauchy's Integral Theorem / 9：
Cauchy's Integral Formula / 10：
Cauchy's Calculus of Residues / 11：
Cauchy on Liouville's Theorem / 13a：
Jordan on Liouville's Theorem / 13b：
Riemann's Influence
Riemann on the Cauchy-Riemann Equations / 13：
Riemann on Riemann Surfaces / 14：
Schwarz on Conformal Mapping / 15：
Convergent Expansions / Part 3：
The Convergence of Power Series
Gauss on the Hypergeometric Series / 16：
Abel on the Binomial Series / 17：
The Influence of Weierstrass
Weierstrass on Analytic Functions of several Variables / 18：
Picard on Picard's Theorem / 19：
Weierstrass on Infinite Products / 20a：
Mittag-Leffier's Theorem / 20b：
Asymptotic Expansions / Part 4：
Analytic Number Theory
Riemann on the Riemann Zeta Function / 21：
Hadamard on the Distribution of Primes / 22：
Asymptotic Series
Stirling's Formula / 23：
Laplace on Generating Functions / 24：
Abel on the Laplace Transform / 25：
Poincare on Asymptotic Series / 26：
Lereh on Lerch's Theorem / 27：
Fourier Series and Integrals / Part 5：
Fourier Series
Fourier on Heat Flow in a Slab / 28：
Fourier on Expansions in Sine Series / 29a：
Fourier on Heat Flow in a Ring / 29b：
Dirichlet on the Convergence of Fourier Series / 30：
Wilbraham on the Gibbs Phenomenon / 31：
Fejre on the Convergence of Fourier Series / 32：
The Fourier Integral
Cauchy on the Fourier Integral / 33a-b：
Fourier on the Fourier Integral / 34：
Cauchy on Linear Partial Differential Equations with Constant Coefficients / 35：
Elliptic and Abelian Integrals / Part 6：
Legendre on Elliptic Integrals / 36：
Abel's Addition Theorem / 37：
Abel on Hyperelliptic Integrals / 38：
Riemann on Abelian Integrals / 39a：
Roch on the Riemann-Roch Theorem / 39b：
Elliptic and Automorphic Functions / Part 7：
Elliptic and Hyperelliptic Functions
Abel on Elliptic Functions / 40：
Jacobi on Elliptic Functions / 41：
Jacobi on Some Identities / 42：
Jacobi on the Jacobi Theta Functions / 43：
Weierstrass's Al Functions / 44：
Automorphic Functions
Poincare on Automorphic Functions / 45：
Klein on Fundamental Regions of Discontinuous Groups / 46：
Ordinary Differential Equations. I. / Part 8：
Existence and Uniqueness Theorems
Cauchy on the Cauchy Polygon Method / 47：
Lipschitz on the Lipschitz Condition / 48：
Picard on the Picard Method / 49：
Osgood's Existence Theorem / 50：
Sturm-Liouville Theory
Storm on Sturm's Theorems / 51：
Liouville on Sturm-Liouville Expansions. I. / 52：
Liouville on Sturm-Liouville Expansions. II. / 53：
Ordinary Differential Equations. II. / Part 9：
Regular Singular Points
Fuchs on Isolated Singular Points / 54：
Frobenius on Regular Singula / 55：
Foundations of Real Analysis / Part 1：
Cauchy's Partial Rigorization / A：
Cauchy on Limits and Continuity / 1a：
63.
図書
Stuart E. Dreyfus, Averill M. Law
64.
図書
Graham J.G. Upton
65.
図書
Dimitri P. Bertsekas
66.
図書
edited by Walter Joh[ann] Ziegler
67.
図書
Philippe G. Ciarlet
目次情報:
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Description of Three-Dimensional Elasticity / Part A：
Geometrical and other preliminaries / 1：
The equations of equilibrium and the principle of virtual work / 2：
Elastic materials and their constitutive equations / 3：
Hyperelasticity / 4：
The boundary value problems of three-dimensional elasticity / 5：
Mathematical Methods in Three-Dimensional Elasticity / Part B：
Existence theory based on the implicit function theorem / 6：
Existence theory based on the minimization of the Energy / 7：
Bibliography
Index
Description of Three-Dimensional Elasticity / Part A：
Geometrical and other preliminaries / 1：
The equations of equilibrium and the principle of virtual work / 2：
68.
図書
Georges de Rham ; translated from the French by F.R. Smith ; introduction to the English edition by S.S. Chern
69.
図書
Sterling K. Berberian
70.
図書
Gregory Karpilovsky
71.
図書
V.S. Pugachev and I.N. Sinitsyn ; translated by I.V. Sinitsyna ; translation editor, V.S. Pugachev
出版情報:
Chichester [West Sussex] ; New York : Wiley, c1987 xx, 549 p. ; 24 cm
子書誌情報:
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72.
図書
Yonathan Bard
出版情報:
New York : Academic Press, 1974 x, 341 p. ; 24 cm
子書誌情報:
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73.
図書
Kurt Strebel
74.
図書
Siegfried Flügge
75.
図書
Glen E. Bredon
76.
図書
Jöran Bergh, Jörgen Löfström
77.
図書
Frederick P. Gardiner
78.
図書
[by] Charles L. Lawson [and] Richard J. Hanson
目次情報:
続きを見る
Preface to the Classics Edition
Preface
Introduction / 1：
Analysis of the Least Squares Problem / 2：
Orthogonal Decomposition by Certain Elementary Orthogonal Transformations / 3：
Orthogonal Decomposition by Singular Value Decomposition / 4：
Perturbation Theorems for Singular Values / 5：
Bounds for the Condition Number of a Triangular Matrix / 6：
The Pseudoinverse / 7：
Perturbation Bounds for the Pseudoinverse / 8：
Perturbation Bounds for the Solution of Problem LS / 9：
Numerical Computations Using Elementary Orthogonal Transformations / 10：
Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem / 11：
Computation of the Covariance Matrix of the Solution Parameters / 12：
Computing the Solution for the Underdetermined Full Rank Problem / 13：
Computing the Solution for Problem LS with Possibly Deficient Pseudorank / 14：
Analysis of Computing Errors for Householder Transformations / 15：
Analysis of Computing Errors for the Problem LS / 16：
Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic / 17：
Computation of the Singular Value Decomposition and the Solution of Problem LS / 18：
Other Methods for Least Squares Problems / 19：
Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space / 20：
Linear Least Squares with Linear Equality Constraints by Direct Elimination / 21：
Linear Least Squares with Linear Equality Constraints by Weighting / 22：
Linear Least Squares with Linear Inequality Constraints / 23：
Modifying a QR Decomposition to Add or Remove Column Vectors / 24：
Practical Analysis of Least Squares Problems / 25：
Examples of Some Methods of Analyzing a Least Squares Problem / 26：
Modifying a QR Decomposition to Add or Remove Row Vectors with Application to Sequential Processing of Problems Having a Large or Banded Coefficient Matrix / 27：
Basic Linear Algebra Including Projections / Appendix A：
Proof of Global Quadratic Convergence of the QR Algorithm / Appendix B：
Description and Use of FORTRAN Codes for Solving Problem LS / Appendix C：
Developments from 1974 to 1995 / Appendix D：
Bibliography
Index
Preface to the Classics Edition
Preface
Introduction / 1：
79.
図書
Shlomo Sternberg
80.
図書
Carl M. Bender, Steven A. Orszag
81.
図書
H. Rademacher ; edited by D. Goldfeld ; notes by G. Crane
出版情報:
Boston : Birkhäuser, c1983 138 p. ; 24 cm
子書誌情報:
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82.
図書
F. Maeda, S. Maeda
83.
図書
by Kenneth J. Arrow, Leonid Hurwicz, Hirofumi Uzawa ; with contributions by Hollis B. Chenery ... [et al.]
84.
図書
Jared L. Cohon
85.
図書
Solomon Lefschetz
86.
図書
R. Courant, K.O. Friedrichs
目次情報:
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Compressible Fluids / I：
Mathematical Theory of Hyperbolic Flow Equations for Functions of Two Variables / II：
One-Dimensional Flow / III：
Isentropic Irrotational Steady Plane Flow / IV：
Flow in Nozzles and Jets / V：
Flow in Three Dimensions / VI：
Compressible Fluids / I：
Mathematical Theory of Hyperbolic Flow Equations for Functions of Two Variables / II：
One-Dimensional Flow / III：
87.
図書
edited by Frederick van der Ploeg
88.
図書
Jun-ichi Igusa
89.
図書
by Edwin F. Beckenbach and Richard Bellman
90.
図書
Kichoon Yang
出版情報:
Singapore : World Scientific, c1987 x, 112 p. ; 23 cm
子書誌情報:
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91.
図書
edited by A.R. Bednarek, L. Cesari
出版情報:
New York : Academic Press, 1977 xv, 516 p. ; 24 cm
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92.
図書
Yu.D. Burago, V.A. Zalgaller ; translated from the Russian by A.B. Sossinsky
93.
図書
Carlo Cercignani
目次情報:
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Basic Principles of the Kinetic Theory of Gases
The Boltzmann Equation
Gas-Surface Interaction and the H-Theorem
Linear Transport
Small and Large Mean Free Paths
Analytical Solutions of Models
The Transition Regime
Theorems on the Solutions of the Boltzmann Equation
Appendix
References
Author Index
Subject Index
Basic Principles of the Kinetic Theory of Gases
The Boltzmann Equation
Gas-Surface Interaction and the H-Theorem
94.
図書
I.R. Shafarevich ; translated from the Russian by K.A. Hirsch
95.
図書
by Salomon Bochner ; translated from the original by Morris Tenenbaum and Harry Pollard
96.
図書
by Claude Chevalley
出版情報:
[Providence, R.I.] : American Mathematical Society, 1951 xi, 188 p. ; 26 cm
シリーズ名:
Mathematical surveys ; no. 6
子書誌情報:
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97.
図書
R. von Mises, K.O. Friedrichs
98.
図書
Theodor Meis, Ulrich Marcowitz ; [translated by Peter R. Wadsack]
99.
図書
Arch W. Naylor, George R. Sell
目次情報:
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Preface
Introduction
Set-Theoretic Structure
Topological Structure
Algebraic Structure
Combined Topological and Algebraic Structure
Analysis of Linear Operators (Compact Case)
Analysis of Unbounded Operators
The Hoelder, Schwartz, and Minkowski Inequalities
Cardinality
Zorn's Lemma
Integration and Measure Theory
Probability Spaces and Stochastic Processes
Index of Symbols
Index
Preface
Introduction
Set-Theoretic Structure
100.
図書
R. Gnanadesikan
目次情報:
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Reduction of Dimensionality
Development and Study of Multivariate Dependencies
Multidimensional Classification and Clustering
Assessment of Specific Aspects of Multivariate Statistical Models
Summarization and Exposure
References
Appendix
Indexes
Reduction of Dimensionality
Development and Study of Multivariate Dependencies
Multidimensional Classification and Clustering
図書
