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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About 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, Winona, MN, in 1962. Dr. Zill is also former chair of the Mathematics Department at Loyola Marymount University. He is also the author or co-author of 13 texts in mathematics.
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13 of 13 people found the following review helpful:
4.0 out of 5 stars
A good text on ordinary differential equations with good examples,
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This review is from: A First Course in Differential Equations: The Classic Fifth Edition (Hardcover)
This particular textbook concerns ordinary differential equations. There are plenty of examples, and they are worked in steps that should make the solution strategy clear to any student with at least two previous semesters of calculus. One of the unusual features of the book are essays written by mathematicians present at the end of chapters 3, 4, 5, and 9. Each essay concerns applications of concepts learned in the previous chapter. The book is well illustrated, and motivations for study are included by making the examples solve practical problems such as the charge on a capacitor, solving orthogonal trajectories of the family of a rectangular hyperbola, or even determining the half-life of a radioactive substance. This makes it ideal for engineering students. There are numerous exercises at the end of each chapter and the solutions to odd numbered problems can be found in the back of the book. The following is the 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
5.0 out of 5 stars
Best Book Out There For ODEs,
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This review is from: A First Course in Differential Equations: The Classic Fifth Edition (Hardcover)
This is the best book I've come across for ordinary differential equations, and I've gone through many of them as a mathematics major! Not only did this book teach me the entire subject matter, I continue to go back to it years later whenever I need to review a technique. The explanations are lucid and clear, and the examples provided are very helpful. Most importantly, when presenting a technique, the authors break it down into all possible cases, so that you are ready to handle any type of problem assigned for hw or tests. I highly recommend this book!
6 of 10 people found the following review helpful:
3.0 out of 5 stars
Beware of the "Example" Problems,
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This review is from: A First Course in Differential Equations: The Classic Fifth Edition (Hardcover)
Overall, the textbook is decent. However, when it comes to reading the example problems in the text, one can, and probably will, become very confused. In my opinion, the purpose of an example problem in the text is to completely break down all the steps towards finding the solution to the problem for the reader, especially one that is a first-timer in DE. This book fails to do so. As a first-timer in DE, I became more confused reading the example problems than I was when perusing the text. The explanations were neither lucid nor thorough enough for my liking. But do not be discouraged first-timers! It is possible to earn your A using this textbook. With the right amount of motivation and study sessions, your A will come. If I could get an A in this class as a college freshman, then anyone could.
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