Differential Equations : Computing and Modeling

by Edwards, C. Henry; Penney, David E.

• ISBN13: 9780130797797
• ISBN10: 0130797790
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-07-01
• Publisher: Prentice Hall

Summary

For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course while maintaining the solid foundation of algebraic techniques that are still essential to science and engineering students. It reflects the new excitement in differential equations as the availability of technical computing environments likeMaple, Mathematica, and MATLAB reshape the role and applications of the discipline. New technology has motivated a shift in emphasis from traditional, manual methods to both qualitative and computer-based methods that render accessible a wider range of realistic applications. With this in mind, the text augments core skills with conceptual perspectives that students will need for the effective use of differential equations in their subsequent work and study.

Table of Contents

Computing Projects	v
Preface	vii
First-Order Differential Equations	1	(74)
Differential Equations and Mathematical Models	1	(9)
Integrals as General and Particular Solutions	10	(8)
Direction Fields and Solution Curves	18	(12)
Separable Equations and Applications	30	(14)
Linear First-Order Equations	44	(14)
Substitution Methods and Exact Equations	58	(17)
Mathematical Models and Numerical Methods	75	(65)
Population Models	75	(13)
Equilibrium Solutions and Stability	88	(6)
Acceleration-Velocity Models	94	(11)
Numerical Approximation: Euler's Method	105	(11)
A Closer Look at the Euler Method	116	(12)
The Runge-Kutta Method	128	(12)
Linear Equations of Higher Order	140	(102)
Introduction: Second-Order Linear Equations	140	(14)
General Solutions of Linear Equations	154	(14)
Homogeneous Equations with Constant Coefficients	168	(12)
Mechanical Vibrations	180	(11)
Nonhomogeneous Equations and the Method of Undetermined Coefficients	191	(16)
Forced Oscillations and Resonance	207	(13)
Electrical Circuits	220	(8)
Endpoint Problems and Eigenvalues	228	(14)
Introduction to Systems of Differential Equations	242	(42)
First-Order Systems and Applications	242	(14)
The Method of Elimination	256	(11)
Numerical Methods for Systems	267	(17)
Linear Systems of Differential Equations	284	(91)
Matrices and Linear Systems	284	(20)
The Eigenvalue Method for Homogeneous Systems	304	(16)
Second-Order Systems and Mechanical Applications	320	(14)
Multiple Eigenvalue Solutions	334	(18)
Matrix Exponentials and Linear Systems	352	(14)
Nonhomogeneous Linear Systems	366	(9)
Nonlinear Systems and Phenomena	375	(70)
Stability and the Phase Plane	375	(13)
Linear and Almost Linear Systems	388	(15)
Ecological Models: Predators and Competitors	403	(13)
Nonlinear Mechanical Systems	416	(16)
Chaos in Dynamical Systems	432	(13)
Laplace Transform Methods	445	(67)
Laplace Transforms and Inverse Transforms	445	(12)
Transformation of Initial Value Problems	457	(12)
Translation and Partial Fractions	469	(10)
Derivatives, Integrals, and Products of Transforms	479	(9)
Periodic and Piecewise Continuous Input Functions	488	(13)
Impulses and Delta Functions	501	(11)
References for Further Study	512	(2)
Appendix: Existence and Uniqueness of Solutions	514	(16)
Answers to Selected Problems	530
Index	1