Introduction to Applied Mathematics (Hardback)

Condition

GOOD: This book would be considered in VERY GOOD condition (showing very little sign of use or wear) except that a previous owner's name is written on the front end page.

Product Details

Also from the Author in the Preface: "Applied mathematics is alive and very rigorous. That ought to be reflected in our teaching. In my own class I became convinced that the textbook is crucial. It must provide a framework into which the applications will fit. A good course has a clear purpose, and you can sense that it is there."

BRIEF CONTENTS

1. Symmetric Linear Systems

1. Introduction
2. Gaussian Elimination
3. Positive Definite Matrices
4. Minimum Principles
5. Eigenvalues and Dynamical Systems
6. A Review of Matrix Theory

2. Equilibrium Equations

1. A Framework for the Applications
2. Constraints and Lagrange Multipliers
3. Electrical Networks
4. Structures in Equilibrium

Least Squares Estimation and the Kalman Filter

3. Equilibrium in the Continuous Case

1. One-dimensional Problems
2. Differential Equations of Equilibrium
3. Laplace's Equation and Potential Flow
4. Vector Calculus in Three Dimensions
5. Equilibrium of Fluids and Solids
6. Calculus of Variations

4. Analytical Methods

1. Fourier Series and Orthogonal Expansions
2. Discrete Fourier Series and Convolution
3. Fourier Integrals
4. Complex Variables and Conformal Mapping
5. Complex Integration

5. Numerical Methods

1. Linear and Nonlinear Equations
2. Orthogonalization and Eigenvalue Problems
3. Semi-direct and Iterative Methods
4. The Finite Element Method
5. The Fast Fourier Transform

6. Initial-Value Problems

1. Ordinary Differential Equations
2. Stability and the Phase Plane and Chaos
3. The Laplace Transform and the z-Transform
4. The Heat Equation vs. the Wave Equation
5. Difference Methods for Initial-Value Problems
6. Nonlinear Conservation Laws

7. Network Flows and Combinatorics

1. Spanning Trees and Shortest Paths
2. The Marriage Problem
3. Matching Algorithms
4. Maximal Flow in a Network

8. Optimization

1. Introduction to Linear Programming
2. The Simplex Method and Karmarkar's Method
3. Duality in Linear Programming
4. Saddle Points (Minimax) and Game Theory
5. Nonlinear Optimization

End Matter A manual for instructors is available from the publisher.