A First Course in Differential Equations: The Classic Fifth Edition / Edition 5

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Overview

The CLASSIC EDITION of Zill's respected book was designed for instructors who prefer not to emphasize technology, modeling, and applications, but instead want to focus on fundamental theory and techniques. Zill's CLASSIC EDITION, a reissue of the fifth edition, offers his excellent writing style, a flexible organization, an accessible level of presentation, and a wide variety of examples and exercises, all of which make it easy to teach from and easy for readers to understand and use.

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Editorial Reviews

Booknews
An undergraduate text covering first-order and higher-order differential equations, series solutions of linear equations, the Laplace transform, systems of linear first-order differential equations, and numerical solutions of ordinary differential equations. This edition has a clearer delineation to the three major approaches to differential equations: analytical, qualitative, and numerical. It includes new problems that call for the use of a computer algebra system, new conceptual and discussion problems, and new project modules. The author is affiliated with Loyola Marymount University. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780534373887
  • Publisher: Cengage Learning
  • Publication date: 12/8/2000
  • Edition description: REV
  • Edition number: 5
  • Pages: 544
  • Sales rank: 419,863
  • Product dimensions: 8.32 (w) x 10.37 (h) x 1.10 (d)

Meet the Author

Dennis G. Zill is professor of mathematics at Loyola Marymount University. His interests are in applied mathematics, special functions, and integral transforms. Dr. Zill received his Ph.D. in applied mathematics and his M.S. from Iowa State University in 1967 and 1964, respectively. He received his B.A. from St. Mary's in Winona, Minnesota, in 1962. Dr. Zill also is former chair of the Mathematics Department at Loyola Marymount University. He is the author or co-author of 13 mathematics texts.

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Table of Contents

1. INTRODUCTION TO DIFFERENTIAL EQUATIONS Basic Definitions and Terminology / Some Mathematical Models / Review / Exercises 2. FIRST-ORDER DIFFERENTIAL EQUATIONS Preliminary Theory / Separable Variables / Homogeneous Equations / Exact Equations / Linear Equations / Equations of Bernoulli, Ricatti, and Clairaut / Substitutions / Picard's Method / Review / Exercises 3. APPLICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS Orthogonal Trajectories / Applications of Linear Equations / Applications of Nonlinear Equations / Review / Exercises / Essay: Population Dynamics 4. LINEAR DIFFERENTIAL EQUATIONS OF HIGHER-ORDER Preliminary Theory / Constructing a Second Solution from a Know Solution / Homogeneous Linear Equations with Constant Coefficients / Undetermined Coefficients: Superposition Approach / Differential Operators / Undetermined Coefficients: Annihilator Approach / Variation of Parameters / Review / Exercises / Essay: Chaos 5. APPLICATIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS: VIBRATIONAL MODELS Simple Harmonic Motion / Damped Motion / Forced Motion / Electric Circuits and Other Analogous Systems / Review / Exercises / Essay: Tacoma Narrows Suspension Bridge Collapse 6. DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS Cauchy-Euler Equation / Review of Power Series; Power Series Solutions / Solutions About Ordinary Points / Solutions About Singular Points / Two Special Equations / Review / Exercises 7. LAPLACE TRANSFORM Laplace Transform / Inverse Transform / Translation Theorems and Derivatives of a Transform / Transforms of Derivatives, Integrals, and Periodic Functions / Applications / Dirac Delta Function / Review / Exercises 8. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS Operator Method / Laplace Transform Method / Systems of Linear First-Order Equations / Introduction to Matrices / Matrices and Systems of Linear First-Order Equations / Homogeneous Linear Systems / Undetermined Coefficients / Variation of Parameters / Matrix Exponential / Review / Exercises 9. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Direction Fields / The Euler Methods / The Three-Term Taylor Method / The Runge-Kutta Methods / Multistep Methods / Errors and Stability / Higher-Order Equations and Systems / Second-Order Boundary-Value Problems / Review / Exercises / Essay: Nerve Impulse Models / APPENDIX I: GAMMA FUNCTION / APPENDIX II: LAPLACE TRANSFORMS / APPENDIX III: REVIEW OF DETERMINANTS / APPENDIX IV: COMPLEX NUMBERS / ANSWERS TO ODD-NUMBERED PROBLEMS

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Sort by: Showing all of 2 Customer Reviews
  • Posted February 6, 2009

    Great for engineering majors!

    I used this textbook for my undergraduate differential equations course. As an engineering major, this course was required. I had an amazing time with this book. If you have a solid foundation in math (more notably calculus I, II, and III) you should be able to grasp the concepts right away. I can honestly say that I could have learned ODE with this textbook by itself, I didn't really have to go to class. That's how well written this book is. I also like how this edition has essays written by mathematicians in their respective fields. The essays are about how the concepts of that chapter are applied to the real world... very interesting material. If you're a math major and looking for a more rigorous book, check Dennis G. Zill's Differential Equations with Boundary-Value Problems.

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  • Anonymous

    Posted August 15, 2009

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