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A First Course in Differential Equations: The Classic Fifth Edition [Hardcover]

Dennis G. Zill
3.0 out of 5 stars  See all reviews (4 customer reviews)
List Price: CDN$ 210.95
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Book Description

Dec 8 2000 0534373887 978-0534373887 5
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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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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Customer Reviews

3.0 out of 5 stars
3.0 out of 5 stars
Most helpful customer reviews
3.0 out of 5 stars School Textbook Feb. 19 2014
By colmex
Format:Hardcover|Verified Purchase
This is the textbook for my university's intro to differential equations class. So far I've found the exercises in the textbook pretty useful and cover a good array of the difficulty of the chapter. The actual examples for each chapter I've found to be not as good as my professor's but nonetheless useful.
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2.0 out of 5 stars Very hard to follow. Sept. 6 2013
By Marco
Format:Hardcover|Verified Purchase
If you're not gifted in math this book is very hard to follow. The theory explanations are good, but the practice problems are extremely hard to follow.
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0 of 2 people found the following review helpful
5.0 out of 5 stars Very happy with my purchase Sept. 21 2011
Format:Hardcover
I bought a book I needed for one of my courses and literally saved more than 100 dollars. shipping was very fast. very happy with my purchase and definitely recommend this seller.
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0 of 3 people found the following review helpful
2.0 out of 5 stars too much theory June 6 2003
By JimBob
Format:Hardcover
they prove EVERY single theorem in the most grating way... good chapters on applications though.
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 3.9 out of 5 stars  30 reviews
24 of 25 people found the following review helpful
4.0 out of 5 stars A good text on ordinary differential equations with good examples Dec 7 2007
By calvinnme - Published on Amazon.com
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. 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
9 of 10 people found the following review helpful
5.0 out of 5 stars Best Book Out There For ODEs Jan. 29 2012
By SamM - Published on Amazon.com
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!
3 of 4 people found the following review helpful
5.0 out of 5 stars keep this book as a reference if you plan on any math, science, or engineering courses Dec 2 2012
By C - Published on Amazon.com
Format:Hardcover
This book came in handy once I started upper-level undergraduate courses in mathematics. 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.
3.0 out of 5 stars Its alright July 30 2014
By Matt - Published on Amazon.com
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
4.0 out of 5 stars Good purchase June 14 2014
By Beauty - Published on Amazon.com
Format:Hardcover|Verified Purchase
The book was in very good condition relatively to the price. There is writing in pencil, but I don't mind it. The book helps me accomplish my performance in the class.
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