Differential Equations: Computing and Modeling / Edition 1

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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.

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Editorial Reviews

This introductory text for science and engineering students is identical to the simultaneously issued Differential Equations and Boundary Value Problems: Computing and Modeling, but is three chapters shorter. Examples and discussion of practical mathematical modeling situations comprise most of the text, with reference to relevant theory. Some 30 computing projects illustrate the use of Maple, Mathematica, and MATLAB. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780133821024
  • Publisher: Prentice Hall Professional Technical Reference
  • Publication date: 10/28/1995
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 502
  • Product dimensions: 8.30 (w) x 9.56 (h) x 0.95 (d)

Table of Contents

1 First-Order Differential Equations 1
2 Mathematical Models and Numerical Methods 69
3 Linear Equations of Higher Order 129
4 Introduction to Systems of Differential Equations 219
5 Linear Systems of Differential Equations 255
6 Nonlinear Systems and Phenomena 333
7 Laplace Transform Methods 397
8 Power Series Methods 457
9 Fourier Series Methods 529
10 Eigenvalues and Boundary Value Problems 599
References for Further Study 663
Appendix 667
Answers to Selected Problems 683
Index I-1
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