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A First Course in Differential Equations: The Classic Fifth Edition (Classic Edition) 5th Edition

3.9 out of 5 stars 44 customer reviews
ISBN-13: 978-0534373887
ISBN-10: 0534373887
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Editorial Reviews

Review

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

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 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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Product Details

  • Series: Classic Edition
  • Hardcover: 520 pages
  • Publisher: Brooks Cole; 5 edition (December 8, 2000)
  • Language: English
  • ISBN-10: 0534373887
  • ISBN-13: 978-0534373887
  • Product Dimensions: 8.3 x 1.1 x 10.4 inches
  • Shipping Weight: 2.6 pounds
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (44 customer reviews)
  • Amazon Best Sellers Rank: #26,654 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

Format: Hardcover Verified Purchase
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.
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Format: 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!
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Format: Hardcover
This book came in handy once I started upper-level undergraduate courses in mathematics (if you choose analysis or applied analysis as your focus). I went back to Zill more than any other textbook that I own, to the point where I have certain pages memorized. It's a really great resource.

Highly recommended.
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Format: Hardcover Verified Purchase
The worst book ever. Also, it teaches in most confusing way. I couldn't understand this book, so I studied from YouTube videos.
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Format: Hardcover Verified Purchase
One of the hardest classes I took in college by far. This was the book that we used for it and it was informative somtimes having to google certain things to get the full grasp on the concept this was a good book to learn from however
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Format: Hardcover Verified Purchase
The book is okay for intro to DiffEq, some of the steps aren't very intuitive, my own professor for the course stared at a few of the steps for a few minutes and deemed them as out of a place for an introductory course(if I didn't send the book back already for my rental I would point them out, but in one of the steps the author says something like "it should be clear why this happens and if it isn't just stare at it long enough until you get it..." or something amount those lines)

and then the author does a few completely ridiculous algebraic manipulations like taking a 2nd derivative of a product and putting it back into the form d^2/dx^2[2x*d/dx[e^(x)]+d/dx[2x]*e^(x)], and then went into factoring it to get what he needed, just some ridiculous manipulations when if he used different examples the point would still be made without unnecessary algebra

and as usual its completely overpriced for how mediocre it is
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Format: Hardcover Verified Purchase
You won't be able to teach yourself with this book alone. Doesn't go into very much depth
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Format: Hardcover Verified Purchase
Great textbook for learning Differential Equations. However, the author does leave out some important notes in the solutions. The author always assume a positive domain in the solution, and leaves out the negative. A math instructor would find that somewhat negligent on the author's behalf.
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