Introduction to applied mathematics

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Introduction to applied mathematics / Gilbert Strang

資料種別:: 図書
出版情報:: Wellesley, Mass. : Wellesley-Cambridge Press, c1986
形態:: ix, 758 p. ; 25 cm
著者名:: Strang, Gilbert, 1934- <DA00732202>
ISBN:: 9780961408800 [0961408804]
書誌ID:: BA00768065

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注記:

Bibliography: p. [738]-739
Includes index

主題:

Mathematics--1961-

言語:

英語

目次情報:

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：

Positive definite matrices / 1.3：

Minimum principles / 1.4：

Eigenvalues and dynamical systems / 1.5：

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