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1.

図書

図書
Gilbert Strang
出版情報: Wellesley, Mass. : Wellesley-Cambridge Press, c1986  ix, 758 p. ; 25 cm
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目次情報: 続きを見る
Symmetric Linear Systems / 1:
Introduction / 1.1:
Gaussian elimination / 1.2:
Positive definite matrices / 1.3:
Minimum principles / 1.4:
Eigenvalues and dynamical systems / 1.5:
A review of matrix theory / 1.6:
Equilibrium Equations / 2:
A framework for the applications / 2.1:
Constraints and Lagrange multipliers / 2.2:
Electrical networks / 2.3:
Structures in equilibrium / 2.4:
Least squares estimation and the Kalman filter / 2.5:
Equilibrium in the Continuous Case / 3:
One-dimensional problems / 3.1:
Differential equations of equilibrium / 3.2:
Laplace's equation and potential flow / 3.3:
Vector calculus in three dimensions / 3.4:
Equilibrium of fluids and solids / 3.5:
Calculus of variations / 3.6:
Analytical Methods / 4:
Fourier series and orthogonal expansions / 4.1:
Discrete Fourier series and convolution / 4.2:
Fourier integrals / 4.3:
Complex variables and conformal mapping / 4.4:
Complex integration / 4.5:
Numerical Methods / 5:
Linear and nonlinear equations / 5.1:
Orthogonalization and eigenvalue problems / 5.2:
Semi-direct and iterative methods / 5.3:
The finite element method / 5.4:
The fast Fourier transform / 5.5:
Initial-Value Problems / 6:
Ordinary differential equations / 6.1:
Stability and the phase plane and chaos / 6.2:
The Laplace transform and the z-transform / 6.3:
The heat equation vs. the wave equation / 6.4:
Difference methods for initial-value problems / 6.5:
Nonlinear conservation laws / 6.6:
Network Flows and Combinatorics / 7:
Spanning trees and shortest paths / 7.1:
The marriage problem / 7.2:
Matching algorithms / 7.3:
Maximal flow in a network / 7.4:
Optimization / 8:
Introduction to linear programming / 8.1:
The simplex method and Karmarkar's method / 8.2:
Duality in linear programming / 8.3:
Saddle points (minimax) and game theory / 8.4:
Nonlinear optimization / 8.5:
Software for scientific computing
References and acknowledgements
Solutions to selected exercises
Index
Symmetric Linear Systems / 1:
Introduction / 1.1:
Gaussian elimination / 1.2:
2.

図書

図書
Gilbert Strang
出版情報: New York : Academic Press, c1976  xi, 374 p. ; 24 cm
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目次情報: 続きを見る
Matrices and Gaussian Elimination / Chapter 1:
Introduction / 1.1:
The Geometry of Linear Equations / 1.2:
An Example of Gaussian Elimination / 1.3:
Matrix Notation and Matrix Multiplication / 1.4:
Triangular Factors and Row Exchanges / 1.5:
Inverses and Transposes / 1.6:
Special Matrices and Applications / 1.7:
Review Exercises: Chapter 1
Vector Spaces / Chapter 2:
Vector Spaces and Subspaces / 2.1:
Solving Ax = 0 and Ax = b / 2.2:
Linear Independence, Basis, and Dimension / 2.3:
The Four Fundamental Subspaces / 2.4:
Graphs and Networks / 2.5:
Linear Transformations / 2.6:
Review Exercises: Chapter 2
Orthogonality / Chapter 3:
Orthogonal Vectors and Subspaces / 3.1:
Cosines and Projections onto Lines / 3.2:
Projections and Least Squares / 3.3:
Orthogonal Bases and Gram-Schmidt / 3.4:
The Fast Fourier Transform / 3.5:
Review Exercises: Chapter 3
Determinants / Chapter 4:
Properties of the Determinant / 4.1:
Formulas for the Determinant / 4.3:
Applications of Determinants / 4.4:
Review Exercises: Chapter 4
Eigenvalues and Eigenvectors / Chapter 5:
Diagonalization of a Matrix / 5.1:
Difference Equations and Powers A[superscript k] / 5.3:
Differential Equations and e[superscript At] / 5.4:
Complex Matrices / 5.5:
Similarity Transformations / 5.6:
Review Exercises: Chapter 5
Positive Definite Matrices / Chapter 6:
Minima, Maxima, and Saddle Points / 6.1:
Tests for Positive Definiteness / 6.2:
Singular Value Decomposition / 6.3:
Minimum Principles / 6.4:
The Finite Element Method / 6.5:
Computations with Matrices / Chapter 7:
Matrix Norm and Condition Number / 7.1:
Computation of Eigenvalues / 7.3:
Iterative Methods for Ax = b / 7.4:
Linear Programming and Game Theory / Chapter 8:
Linear Inequalities / 8.1:
The Simplex Method / 8.2:
The Dual Problem / 8.3:
Network Models / 8.4:
Game Theory / 8.5:
Intersection, Sum, and Product of Spaces / Appendix A:
The Jordan Form / Appendix B:
Solutions to Selected Exercises
Matrix Factorizations
Matrices and Gaussian Elimination / Chapter 1:
Introduction / 1.1:
The Geometry of Linear Equations / 1.2:
3.

図書

図書
G.ストラング, T.グエン共著 ; 高橋進一, 池原雅章共訳
出版情報: 東京 : 培風館, 1999.7  2冊 ; 22cm
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4.

図書

図書
Gilbert Strang
出版情報: Wellesley, Mass. : Wellesley-Cambridge Press, c2007  xi, 716 p. ; 27 cm
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目次情報: 続きを見る
Applied Linear Algebra / 1:
Four special matrices / 1.1:
Differences, derivatives, and boundary conditions / 1.2:
Elimination leads to K = LDL^T / 1.3:
Inverses and delta functions / 1.4:
Eigenvalues and eigenvectors / 1.5:
Positive definite matrices / 1.6:
Numerical linear algebra: LU, QR, SVD / 1.7:
Best basis from the SVD / 1.8:
A Framework for Applied Mathematics / 2:
Equilibrium and the stiffness matrix / 2.1:
Oscillation by Newton's law / 2.2:
Least squares for rectangular matrices / 2.3:
Graph models and Kirchhoff's laws / 2.4:
Networks and transfer functions / 2.5:
Nonlinear problems / 2.6:
Structures in equilibrium / 2.7:
Covariances and recursive least squares / 2.8:
Graph cuts and gene clustering / 2.9:
Boundary Value Problems / 3:
Differential equations of equilibrium / 3.1:
Cubic splines and fourth order equations / 3.2:
Gradient and divergence / 3.3:
Laplace's equation / 3.4:
Finite differences and fast Poisson solvers / 3.5:
The finite element method / 3.6:
Elasticity and solid mechanics / 3.7:
Fourier Series and Integrals / 4:
Fourier series for periodic functions / 4.1:
Chebyshev, Legendre, and Bessel / 4.2:
The discrete Fourier transform and the FFT / 4.3:
Convolution and signal processing / 4.4:
Fourier integrals / 4.5:
Deconvolution and integral equations / 4.6:
Wavelets and signal processing / 4.7:
Analytic Functions / 5:
Taylor series and complex integration / 5.1:
Famous functions and great theorems / 5.2:
The Laplace transform and z-transform / 5.3:
Spectral methods of exponential accuracy / 5.4:
Initial Value Problems / 6:
Introduction / 6.1:
Finite difference methods for ODEs / 6.2:
Accuracy and stability for u_t = c u_x / 6.3:
The wave equation and staggered leapfrog / 6.4:
Diffusion, convection, and finance / 6.5:
Nonlinear flow and conservation laws / 6.6:
Fluid mechanics and Navier-Stokes / 6.7:
Level sets and fast marching / 6.8:
Solving Large Systems / 7:
Elimination with reordering / 7.1:
Iterative methods / 7.2:
Multigrid methods / 7.3:
Conjugate gradients and Krylov subspaces / 7.4:
Optimization and Minimum Principles / 8:
Two fundamental examples / 8.1:
Regularized least squares / 8.2:
Calculus of variations / 8.3:
Errors in projections and eigenvalues / 8.4:
The Saddle Point Stokes problem / 8.5:
Linear programming and duality / 8.6:
Adjoint methods in design / 8.7:
Applied Linear Algebra / 1:
Four special matrices / 1.1:
Differences, derivatives, and boundary conditions / 1.2:
5.

図書

図書
Gilbert Strang
出版情報: Wellesley, Mass. : Wellesley-Cambridge, c2010  1 v. (various pagings) ; 27 cm
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Highlights of calculus
Introduction to calculus / 1:
Derivatives / 2:
Applications of the derivative / 3:
The chain rule / 4:
Integrals / 5:
Exponentials and logarithms / 6:
Techniques of integration / 7:
Applications of the integral / 8:
Polar coordinates and complex numbers / 9:
Infinite series / 10:
Vectors and matrices / 11:
Motion along a curve / 12:
Partial derivatives / 13:
Multiple integrals / 14:
Vector calculus / 15:
Mathematics after calculus / 16:
Highlights of calculus
Introduction to calculus / 1:
Derivatives / 2:
6.

図書

図書
ギルバート・ストラング著 ; 日本応用数理学会監訳
出版情報: 東京 : 近代科学社, 2017.1  xiii, 735p ; 27cm
シリーズ名: 世界標準MIT教科書
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目次情報: 続きを見る
第1章 : 応用線形代数
第2章 : 応用数学の枠組み
第3章 : 境界値問題
第4章 : フーリエ級数とフーリエ変換
第5章 : 解析関数
第6章 : 初期値問題
第7章 : 大規模連立1次方程式の解法
第8章 : 最適化と最小原理
第1章 : 応用線形代数
第2章 : 応用数学の枠組み
第3章 : 境界値問題
概要: 応用数理の体系を示す!
7.

図書

図書
Gilbert Strang
出版情報: Wellesley, MA : Wellesley-Cambridge Press, c2019  xiii, 432 p. ; 25 cm
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8.

図書

図書
ギルバート・ストラング著 ; 渡辺辰矢訳
出版情報: 東京 : 近代科学社, 2017.11  xii, 521p ; 27cm
シリーズ名: 世界標準MIT教科書
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目次情報: 続きを見る
第1章 : 1階常微分方程式
第2章 : 2階常微分方程式
第3章 : 図的および数値的方法
第4章 : 連立一次方程式と逆行列
第5章 : ベクトル空間と部分空間
第6章 : 固有値と固有ベクトル
第7章 : 応用数学とATA
第8章 : フーリエ変換とラプラス変換
行列の分解
行列式の性質
線形代数早わかり
第1章 : 1階常微分方程式
第2章 : 2階常微分方程式
第3章 : 図的および数値的方法
9.

図書

図書
G.ストラング, G.J.フィックス共著 ; 三好哲彦, 藤井宏共訳
出版情報: 東京 : 培風館, 1976.4  x, 328p ; 22cm
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10.

図書

図書
G.ストラング著 ; 井上昭訳
出版情報: 東京 : 産業図書, 1978.7  vii, 431p ; 22cm
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