Differential Equations Demystified (Paperback)

~ Steven Krantz (Author) "A differential equation is an equation relating some function f to one or more of its derivatives..." (more)
Key Phrases: total discretization error, two solution sets, sine series expansion, Math Note, Power Series Solutions, Find the Fourier (more...)

Editorial Reviews

Review

...an important subject...serious, straightforward work...emphasis is consistently...on...computations needed to find...solutions to specific equations... -- Choice, February 2005

explanations, models...examples that lead from differential equations to higher math concepts in a self-paced format...includes solutions to…exercises and…final -- Sci-Tech Book News, Dec. 2004

Review

Krantz asserts that if calculus is the heart of modern science, differential equations are the guts. Writing for those who already have a basic grasp of calculus, Krantz provides explanations, models, and examples that lead from differential equations to higher math concepts in a self-paced format. He includes chapters on first-order and second-order equations, power series solutions and spatial functions, Fourier series, Laplace transforms, numerical methods, partial equations and boundary value problems. His models come from engineering, physics and other fields in math. He includes solutions to the exercises and a final exam. (Sci-Tech Book News )

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Product Details

• Paperback: 323 pages
• Publisher: McGraw-Hill Professional; 1 edition (August 24, 2004)
• Language: English
• ISBN-10: 0071440259
• ISBN-13: 978-0071440257
• Product Dimensions: 9 x 7.3 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.2 out of 5 stars  See all reviews (8 customer reviews)
• Amazon.com Sales Rank: #87,352 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

50 of 55 people found the following review helpful:

3.0 out of 5 stars Not as Bad As Calc Demystified, August 16, 2005

By	Aaron Rutledge - See all my reviews (REAL NAME)

Differential Equations Demystified is written by Steven Krantz, the author of the not-so-popular Calculus Demystified. Admittedly, this book is not any more user friendly than Calculus demystified; he spends no time explaining jargon in informal language; he constantly uses different notation for derivatives, etc. But at this level, at least, it is more acceptable. Any reader tackling the subject of differential equations with any seriousness will have to face rigors of mathematical language at some point.

Surprisingly Krantz claims in his introduction that anyone who has finished Caculus Demystified will be prepared for this book. Unfortunately by page fifteen he is using concepts from multivariable calculus (partial derivatives) that, if I'm not mistaken, were not covered in Calculus Demystified. Unless you are confident in your mathematical skills I would recommend brushing up your multivariable calculus before tackling this text.

For the most part, however, the book proceeds in typical fashion. The reader will be introduced to most of the key topics covered in a typical college Diff Eq class including first and second order differential equations, series solutions, and other basic topics. If you're just looking to get the "flavor" of Diff. Eqs then this book will suffice. However, do not expect to come away from this book with a deep knowledge of the subject matter. He concisely covers most of the basic procedures for solving and manipulating standard ordinary differential equations, and doesn't bog the reader down in much theory. Answers are provided in the back of the book for most of the problems in each chapter.

However, for readers who want a more thorough introductory look at applied differential equations I know of no better introduction than Tenenbaum's Ordinary Differential Equations. Tenenbaum does an excellent job of introducing the theory behind the equations and covers many of the fine details that Krantz leaves out. Another strength of Tenenbaum is his resistance to undue formalism. He takes the time to flesh out the motivation behind each topic with historical asides and physical applications. Krantz does not do this. Seeing as both books are selling for the roughly the same price [...] I see little justification in recommending this work over Tenenbaum's. The only circumstance under which I would recommend Krantz is to the reader who needs a concise and breezy introduction to the methods of Differential Equations. For deeper understanding consult Tenenbaum. And if you are looking for a source for solved practice problems I would direct you to Differential Equations Prolem Solver which has thousands of solved problems.

Overall, a solid, concise effort. But when compared to other books in its league like "Calculus for Dummies" and "How to Ace Calculus" it falls a bit short.

PS: For a great informal brush up on Multivariable caclus I recommend "How to Ace the rest of Caculus".

28 of 31 people found the following review helpful:

5.0 out of 5 stars Perfect for my application, August 23, 2005

By	Crom B. Campbell "prof" (South Texas) - See all my reviews (REAL NAME)

I teach this subject. The book is perfect for a first course whose purpose is to introduce foundational topics from both ordinary and partial differential equations. Not a lot of theory, but I find that the theory undergirding a technique is a lot more palatable when the student has confidence in his ability to use that technique in practice. DE Demystified gets right to the point, presents the method, and then gives examples and practice problems. I learn math by doing it and this book is just what I was looking for. Several other books are available in the classroom for students who choose to go more in depth on any particular topic, and I use other resources for additional problems and to code programs for numerical solutions. But this is the book the students must buy and bring to class. I really like the presentation in DE Demystified.

10 of 11 people found the following review helpful:

5.0 out of 5 stars Excellent, April 30, 2006

By	J. Moody (St. Louis, MO USA) - See all my reviews (REAL NAME)

I bought this book because I am considering getting a graduate degree in math, so I thought it would be useful as a book to brush up with. This book is highly readable and the examples are laid out well. There are ample exercises to test your knowledge of the various techniques for solving diff eqs, answers are included also. It is quite a bit better than the text that was used in engineering school.