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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. The features include: 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 equations; exponential generating functions; and many new examples and exercises.
| ISBN | 012403330X | | Pages | 403 | | ISBN13 | 9780124033306
(What's this?) | | Volumes | 1 | | Publisher | Elsevier Science Publishing Co Inc | | Weight (grammes) | 753 | | Imprint | Academic Press Inc | | Published in | San Diego | | Format | Hardback | | Previous ISBN | 9780124033252 | | Publication date | 16 Jun 2000 | | Height (mm) | 235 | | Non-book description | ix, 403 p. : | | Width (mm) | 165 | | Library of Congress | 99069847 | | Spine width (mm) | 29 | | DEWEY | 515.625 | | Academic level | Tertiary education | | DEWEY edition | DC21 | |
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| | | Preface | | | | Ch. 1 | | Introduction | | 1 | | Ch. 2 | | The Difference Calculus | | 13 | | Sect. 2.1 | | The Difference Operator | | 13 | | Sect. 2.2 | | Summation | | 20 | | Sect. 2.3 | | Generating Functions and Approximate Summation | | 29 | | Ch. 3 | | Linear Difference Equations | | 43 | | Sect. 3.1 | | First Order Equations | | 43 | | Sect. 3.2 | | General Results for Linear Equations | | 50 | | Sect. 3.3 | | Solving Linear Equations | | 54 | | Sect. 3.4 | | Applications | | 63 | | Sect. 3.5 | | Equations with Variable Coefficients | | 75 | | Sect. 3.6 | | Nonlinear Equations That Can Be Linearized | | 82 | | Sect. 3.7 | | The z-Transform | | 86 | | Ch. 4 | | Stability Theory | | 125 | | Sect. 4.1 | | Initial Value Problems for Linear Systems | | 125 | | Sect. 4.2 | | Stability of Linear Systems | | 133 | | Sect. 4.3 | | Phase Plane Analysis for Linear Systems | | 141 | | Sect. 4.4 | | Fundamental Matrices and Floquet Theory | | 150 | | Sect. 4.5 | | Stability of Nonlinear Systems | | 159 | | Sect. 4.6 | | Chaotic Behavior | | 173 | | Ch. 5 | | Asymptotic Methods | | 195 | | Sect. 5.1 | | Introduction | | 195 | | Sect. 5.2 | | Asymptotic Analysis of Sums | | 199 | | Sect. 5.3 | | Linear Equations | | 205 | | Sect. 5.4 | | Nonlinear Equations | | 215 | | | More... | | |
"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  Be the first to write a customer review
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