9780961408800

Introduction to Applied Mathematics

by
  • ISBN13:

    9780961408800

  • ISBN10:

    0961408804

  • Format: Hardcover
  • Copyright: 1986-01-01
  • Publisher: Wellesley Cambridge Pr

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Supplemental Materials

What is included with this book?

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
Table of Contents provided by Publisher. All Rights Reserved.

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