Customer Reviews

A First Course in Differential Equations: The Classic Fifth Edition

5 star:		(6)
4 star:		(2)
3 star:		(1)
2 star:		(2)
1 star:		(1)

 

 

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

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!

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.

This is great book for someone who have problem to get concept of Math.
Easy to Understand and well describe.
Highly recommend.

I am very pleased with my order. It is a brand new differential equations book and it was shipped very fast. Thank you, and I look forward to ordering more from you again!

Quite frankly this is the worst math textbook that I've ever come across. I find it impossible to learn from. As is mentioned in the preface, the authors of the book intentionally refrained from highlighting important information in each chapter. This is an annoyance which I could forgive if they did even a half decent job of introducing the material to the student in each section. They do not.
In order to understand a concept students need to know why that concept is relevant, what its applications are, and how to apply that concept. This text does not adequately do any of that. What it does do is give the student a headache and nothing to show for it.
Each section introduces a technique, basically by saying "here is a technique". The technique is then described in math jargon that is difficult to translate. The authors tend to interrupt their own thoughts with useless information that is distracting. And then you get to the end of the section having learned nothing, but having gained a headache, and there are a bunch of practice problems that you can perhaps solve, not because you read the section but because you already know how to do calculus, but you have no idea why you are solving them. Repeat.

All in all, trying to learn from this textbook is akin to trying to assemble a 100 piece puzzle, but having to dig the puzzle pieces you want out of a pool filled with puzzle pieces, while not being supplied with any way to distinguish the puzzle pieces you want from the ones you don't. You will give yourself a headache sifting through a bunch of irrelevant information, half of which you can't understand because it is written so poorly, in a vain attempt to find something that you can use, and never knowing why you want to use it in the first place.

This book is an utter waste of money, and I will never purchase another book from this publisher - their reputation is ruined by publishing a book of this quality.

The book was in excellent condition. It was also priced very reasonably. Purchasing it here instead of the bookstore saved me over 100 dollars.

Simply straight forward mathematics. Hard for a non-nerd-_by_birth to desire to crack this text. Only the grade kept me going all semester (ended with B).
To be clear though, I have not yet found an interesting Diff Eq text!

Good luck,

I ordered this book and had it within 3 days. Way before it was promised and it was in excellent condition. I would highly recommend doing business with this seller.

delivery took a while because it had to be shipped from overseas, but it arrived in great condition.