Introduction to Applied Mathematics

by Strang, Gilbert

• ISBN13: 9780961408800
• ISBN10: 0961408804
• Format: Hardcover
• Copyright: 1986-01-01
• Publisher: Wellesley Cambridge Pr

Summary

Renowned applied mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and Kalman filtering and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians. The only prerequisite is a basic course in linear algebra.

Table of Contents

Symmetric Linear Systems

Introduction

Gaussian elimination

Positive definite matrices

Minimum principles

Eigenvalues and dynamical systems

A review of matrix theory

Equilibrium Equations

A framework for the applications

Constraints and Lagrange multipliers

Electrical networks

Structures in equilibrium

Least squares estimation and the Kalman filter

Equilibrium in the Continuous Case

One-dimensional problems

Differential equations of equilibrium

Laplace's equation and potential flow

Vector calculus in three dimensions

Equilibrium of fluids and solids

Calculus of variations

Analytical Methods

Fourier series and orthogonal expansions

Discrete Fourier series and convolution

Fourier integrals

Complex variables and conformal mapping

Complex integration

Numerical Methods

Linear and nonlinear equations

Orthogonalization and eigenvalue problems

Semi-direct and iterative methods

The finite element method

The fast Fourier transform

Initial-Value Problems

Ordinary differential equations

Stability and the phase plane and chaos

The Laplace transform and the z-transform

The heat equation vs. the wave equation

Difference methods for initial-value problems

Nonlinear conservation laws

Network Flows and Combinatorics

Spanning trees and shortest paths

The marriage problem

Matching algorithms

Maximal flow in a network

Optimization

Introduction to linear programming

The simplex method and Karmarkar's method

Duality in linear programming

Saddle points (minimax) and game theory

Nonlinear optimization

Software for scientific computing

References and acknowledgements

Solutions to selected exercises

Index

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