Description
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
- Introduction
- Gaussian Elimination
- Positive Definite Matrices
- Minimum Principles
- Eigenvalues and Dynamical Systems
- A Review of Matrix Theory
2. Equilibrium Equations
- A Framework for the Applications
- Constraints and Lagrange Multipliers
- Electrical Networks
- Structures in Equilibrium
- Least Squares Estimation and the Kalman Filter
3. 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
4. Analytical Methods
- Fourier Series and Orthogonal Expansions
- Discrete Fourier Series and Convolution
- Fourier Integrals
- Complex Variables and Conformal Mapping
- Complex Integration
5. Numerical Methods
- Linear and Nonlinear Equations
- Orthogonalization and Eigenvalue Problems
- Semi-direct and Iterative Methods
- The Finite Element Method
- The Fast Fourier Transform
6. 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
7. Network Flows and Combinatorics
- Spanning Trees and Shortest Paths
- The Marriage Problem
- Matching Algorithms
- Maximal Flow in a Network
8. Optimization
- Introduction to Linear Programming
- The Simplex Method and Karmarkar’s Method
- Duality in Linear Programming
- Saddle Points (Minimax) and Game Theory
- Nonlinear Optimization
End Matter
- Appendix: Software for Scientific Computing
- References and Acknowledgements
- Solutions to Selected Exercises
- Index
A manual for instructors is available from the publisher.