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Introduction to Applied Mathematics

Introduction to Applied Mathematics - 86 edition

ISBN13: 978-0961408800

Cover of Introduction to Applied Mathematics 86 (ISBN 978-0961408800)
ISBN13: 978-0961408800
ISBN10: 0961408804
Cover type:
Edition/Copyright: 86
Publisher: Wellesley-Cambridge Press
Published: 1986
International: No
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Introduction to Applied Mathematics - 86 edition

ISBN13: 978-0961408800

Gilbert Strang

ISBN13: 978-0961408800
ISBN10: 0961408804
Cover type:
Edition/Copyright: 86
Publisher: Wellesley-Cambridge Press

Published: 1986
International: No
Summary

This is the textbook for the MIT courses 18.085 and 18.086 on Applied and Engineering Mathematics.

Table of Contents

1. Symmetric Linear Systems

1.1 Introduction
1.2 Gaussian Elimination
1.3 Positive Definite Matrices
1.4 Minimum Principles
1.5 Eigenvalues and Dynamical Systems
1.6 A Review of Matrix Theory

2. Equilibrium Equations

2.1 A Framework for the Applications
2.2 Constraints and Lagrange Multipliers
2.3 Electrical Networks
2.4 Structures in Equilibrium
2.5 Least Squares Estimation and the Kalman Filter

3. Equilibrium in the Continuous Case

3.1 One-dimensional Problems
3.2 Differential Equations of Equilibrium
3.3 Laplace's Equation and Potential Flow
3.4 Vector Calculus in Three Dimensions
3.5 Equilibrium of Fluids and Solids
3.6 Calculus of Variations

4. Analytical Methods

4.1 Fourier Series and Orthogonal Expansions
4.2 Discrete Fourier Series and Convolution
4.3 Fourier Integrals
4.4 Complex Variables and Conformal Mapping
4.5 Complex Integration

5. Numerical Methods

5.1 Linear and Nonlinear Equations
5.2 Orthogonalization and Eigenvalue Problems
5.3 Semi-direct and Iterative Methods
5.4 The Finite Element Method
5.5 The Fast Fourier Transform

6. Initial-Value Problems

6.1 Ordinary Differential Equations
6.2 Stability and the Phase Plane and Chaos
6.3 The Laplace Transform and the z-Transform
6.4 The Heat Equation vs. the Wave Equation
6.5 Difference Methods for Initial-Value Problems
6.6 Nonlinear Conservation Laws

7. Network Flows and Combinatorics

7.1 Spanning Trees and Shortest Paths
7.2 The Marriage Problem
7.3 Matching Algorithms
7.4 Maximal Flow in a Network

8. Optimization

8.1 Introduction to Linear Programming
8.2 The Simplex Method and Karmarkar's Method
8.3 Duality in Linear Programming
8.4 Saddle Points (Minimax) and Game Theory
8.5 Nonlinear Optimization


Software for Scientific Computing
References and Acknowledgements
Solutions to Selected Exercises
Index


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