Difference Equations

An Introduction with Applications

By: Walter G. Kelley, Allan C. Peterson

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Hardcover | 1 May 2000 | Edition Number 2

At a Glance

Hardcover
403 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 16.51 x 1.91

Hardcover

$345.75

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Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.

Phase plane analysis for systems of two linear equations
Use of equations of variation to approximate solutions
Fundamental matrices and Floquet theory for periodic systems
LaSalle invariance theorem
Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
Appendix on the use of Mathematica for analyzing difference equaitons
Exponential generating functions
Many new examples and exercises

Industry Reviews

"The first edition of this book has been the best introduction to difference equations available; the second edition improves this even further." --Martin Bohner, University of Missouri-Rolla "The authors have their finger on the current trends in difference equations. This is a well-written textbook by authors who are known as teachers and expositors." --Johnny Henderson, Auburn University

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Applied Mathematics Combinatorics & Graph Theory Algebra Numerical Analysis

Preface	p. vii
Introduction	p. 1
The Difference Calculus	p. 13
The Difference Operator	p. 13
Summation	p. 20
Generating Functions and Approximate Summation	p. 29
Linear Difference Equations	p. 43
First Order Equations	p. 43
General Results for Linear Equations	p. 50
Solving Linear Equations	p. 54
Applications	p. 63
Equations with Variable Coefficients	p. 75
Nonlinear Equations That Can Be Linearized	p. 82
The z-Transform	p. 86
Stability Theory	p. 125
Initial Value Problems for Linear Systems	p. 125
Stability of Linear Systems	p. 133
Phase Plane Analysis for Linear Systems	p. 141
Fundamental Matrices and Floquet Theory	p. 150
Stability of Nonlinear Systems	p. 159
Chaotic Behavior	p. 173
Asymptotic Methods	p. 195
Introduction	p. 195
Asymptotic Analysis of Sums	p. 199
Linear Equations	p. 205
Nonlinear Equations	p. 215
The Self-Adjoint Second Order Linear Equation	p. 229
Introduction	p. 229
Sturmian Theory	p. 239
Green's Functions	p. 243
Disconjugacy	p. 250
The Riccati Equation	p. 258
Oscillation	p. 265
The Sturm-Liouville Problem	p. 279
Introduction	p. 279
Finite Fourier Analysis	p. 282
Nonhomogeneous Problem	p. 289
Discrete Calculus of Variations	p. 301
Introduction	p. 301
Necessary Conditions	p. 302
Sufficient Conditions and Disconjugacy	p. 312
Boundary Value Problems for Nonlinear Equations	p. 327
Introduction	p. 327
The Lipschitz Case	p. 329
Existence of Solutions	p. 335
Boundary Value Problems for Differential Equations	p. 341
Partial Difference Equations	p. 349
Discretization of Partial Differential Equations	p. 349
Solutions of Partial Difference Equations	p. 356
Appendix	p. 367
Answers to Selected Problems	p. 373
References	p. 383
Index	p. 401
Table of Contents provided by Syndetics. All Rights Reserved.

Difference Equations

An Introduction with Applications

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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