Introduction to Differential Equations

Introduction to Differential Equations, 2/e

Richard Miller, Iowa State University

Published March, 1998 by Prentice Hall Engineering/Science/Mathematics

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Differential Equations-Mathematics

Summary

A thorough examination of the classical topics of differential equations, contemporary models and applications, and areas of theoretical research.

Features

focuses on the practical theories of differential equations and examines both traditional and modern examples of applications — to mechanical problems, chemical kinetics, economics, business, biology, ecology, control theory, electromagnetic theory, elasticity, acoustics, and quantum mechanics.
emphasizes the modeling process and explains the underlying physical assumptions.
offers a complete introduction to sign analysis, error analysis problems, and the Volterra — Lotka predator — prey model.
provides an extensive review of complex numbers infinite series, and the matrix theory.
includes a detailed discussions of delta functions and their approximation in mechanics laboratories using impulse hammers.
explores in-depth the control theory, applications of Laplace transforms to integral equations, and the solution of periodically forced differential equations.

Table of Contents

1. Introduction.
2. First-Order Equations.
3. Second-Order Equations.
4. Linear Equations of Arbitrary Order.
5. Series Solutions of Differential Equations.
6. The Laplace Transform and Its Uses.
7. Systems of Linear Equations.
8. Numerical Methods.
9. Qualitative Analysis.
10. Fourier Series.
11. Separation of Variables.
References.
Answers to Selected Problems.
Index.