Differential Equations: Computing and Modeling / Edition 1

Differential Equations: Computing and Modeling / Edition 1

by C. Henry Edwards, David E. Penny
     
 

ISBN-10: 0133821021

ISBN-13: 9780133821024

Pub. Date: 10/28/1995

Publisher: Prentice Hall Professional Technical Reference

A back–to–basics course is stressed. The computer permits the cutting of highly specialized ODEs to focus in greater depth, from a mathematical perspective, on the core ideas.

Offers an unusually early introduction to mathematical modeling, stability and qualitative properties of differential equations and

Overview

A back–to–basics course is stressed. The computer permits the cutting of highly specialized ODEs to focus in greater depth, from a mathematical perspective, on the core ideas.

Offers an unusually early introduction to mathematical modeling, stability and qualitative properties of differential equations and to numerical methods (Ch. 2).

A qualitative approach is stressed throughout by emphasizing dynamical systems and phase portraits.

Provides an unusually flexible treatment of linear systems:

  • Ch. 4 offers an early, intuitive introduction to first-order systems, models, and numerical computer methods. Includes numerical algorithms presented in parallel fashion for systems ranging from the TI-85 graphics calculator to MATLAB.
  • Ch. 5 begins with a self-contained treatment of the necessary linear algebra, and then presents the eigenvalue approach to linear systems. Includes an large number of applications (ranging from railway cars to earthquakes) of all the various cases of the eigenvalue method.

Presents a broad discussion of nonlinear systems and phenomena -- ranging from phase plane analysis to ecological and mechanical systems to an innovative concluding section on chaos and bifurcation in dynamical systems.

  • presents an elementary introduction to such contemporary topics such as period-doubling in biological and mechanical systems, the pitchfork diagram, and the Lorenz strange attractor -- all illustrated with vivid computer graphics.

Shows how the ready availability of computational aids can clarify traditional manual topics (i.e. undetermined coefficients and Laplace transforms).

Brings numeric and symbolic solutions of differential equations to life -- features 180 computer-generated graphics that vividly illustrate slope fields, solution curves, and phase plane portraits.

Contains approximately 2,000 carefully graded problems -- ranging from routine computational exercises to conceptual and applied problems.

Contains three dozen Computer Projects that illustrate the use of computer algebra systems (e.g., Maple, Mathematica, and MATLAB) -- to actively engage students in the application of new technology.

Product Details

ISBN-13:
9780133821024
Publisher:
Prentice Hall Professional Technical Reference
Publication date:
10/28/1995
Edition description:
Older Edition
Pages:
502
Product dimensions:
8.30(w) x 9.56(h) x 0.95(d)

Table of Contents

Preface ix
1 First-Order Differential Equations
1(68)
1.1 Differential Equations and Mathematical Models
1(9)
1.2 Integrals as General and Particular Solutions
10(7)
1.3 Slope Fields and Solution Curves
17(10)
1.4 Separable Equations and Applications
27(14)
1.5 Linear First-Order Equations
41(11)
1.6 Substitution Methods and Exact Equations
52(13)
Chapter 1 Summary
65(4)
2 Mathematical Models and Numerical Methods
69(60)
2.1 Population Models
69(11)
2.2 Equilibrium Solutions and Stability
80(6)
2.3 Acceleration-Velocity Models
86(13)
2.4 Numerical Approximation: Euler's Method
96(9)
2.5 A Closer Look at the Euler Method
105(12)
2.6 The Runge-Kutta Method
117(12)
3 Linear Equations of Higher Order
129(90)
3.1 Introduction: Second-Order Linear Equations
129(12)
3.2 General Solutions of Linear Equations
141(11)
3.3 Homogeneous Equations with Constant Coefficients
152(11)
3.4 Mechanical Vibrations
163(10)
3.5 Nonhomogeneous Equations and the Methods of Undetermined Coefficients
173(14)
*3.6 Forced Oscillations and Resonance
187(11)
*3.7 Electrical Circuits
198(7)
*3.8 Endpoint Problems and Eigenvalues
205(14)
4 Introduction to Systems of Differential Equations
219(36)
4.1 First-Order Systems and Applications
219(10)
4.2 The Method of Elimination
229(11)
4.3 Numerical Methods for Systems
240(15)
5 Linear Systems of Differential Equations
255(78)
5.1 Matrices and Linear Systems
255(21)
5.2 The Eigenvalue Method for Homogeneous Systems
276(15)
*5.3 Second-Order Systems and Mechanical Applications
291(13)
5.4 Multiple Eigenvalue Solutions
304(16)
*5.5 Matrix Exponentials and Linear Systems
320(13)
6 Nonlinear Systems and Phenomena
333(64)
6.1 Stability and the Phase Plane
333(12)
6.2 Liear and Almost Linear Systems
345(13)
6.3 Ecological Applications: Predators and Competitors
358(11)
6.4 Nonlinear Mechanical Systems
369(14)
6.5 Chaos in Dynamical Systems
383(14)
7 Laplace Transform Methods
397(60)
7.1 Laplace Transforms and Inverse Transforms
397(11)
7.2 Transformation of Initial Value Problems
408(10)
7.3 Translation and Partial Fractions
418(9)
7.4 Derivatives, Integrals, and Products of Transforms
427(8)
*7.5 Periodic and Piecewise Continuous Input Functions
435(12)
7.6 Impulses and Delta Functions
447(10)
References for Further Study 457(4)
Appendix 461(16)
Answers to Selected Problems 477
Index I-1

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >