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Differential Equations with Boundary Value Problems (Hardcover)

~ Selwyn Hollis (Author)
5.0 out of 5 stars  See all reviews (1 customer review)

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Editorial Reviews

Product Description

This book provides readers with a solid introduction to differential equations and their applications emphasizing analytical, qualitative, and numerical methods. Numerical methods are presented early in the text, including a discussion of error estimates for the Euler, Heun, and Runge-Kutta methods. Systems and the phase plane are also introduced early, first in the context of pairs first-order equations, and then in the context of second-order linear equations. Other chapter topics include the Laplace transform, linear first-order systems, geometry of autonomous systems in the plane, nonlinear systems in applications, diffusion problems and Fourier series, and further topics in PDEs.

From the Back Cover

This book provides readers with a solid introduction to differential equations and their applications emphasizing analytical, qualitative, and numerical methods. Numerical methods are presented early in the text, including a discussion of error estimates for the Euler, Heun, and Runge-Kutta methods. Systems and the phase plane are also introduced early, first in the context of pairs first-order equations, and then in the context of second-order linear equations. Other chapter topics include the Laplace transform, linear first-order systems, geometry of autonomous systems in the plane, nonlinear systems in applications, diffusion problems and Fourier series, and further topics in PDEs.
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Product Details

  • Hardcover: 635 pages
  • Publisher: Prentice Hall; 1st edition (January 15, 2002)
  • Language: English
  • ISBN-10: 0130159271
  • ISBN-13: 978-0130159274
  • Product Dimensions: 9.5 x 7.3 x 1.2 inches
  • Shipping Weight: 2.4 pounds
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon.com Sales Rank: #1,734,610 in Books (See Bestsellers in Books)

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More About the Author

Selwyn L. Hollis
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7 of 7 people found the following review helpful:
5.0 out of 5 stars Extraordinary Introduction to DE, July 31, 2003
By Bob Matthews "Dr. Bob" (Raleigh, NC United States) - See all my reviews
Dr. Hollis here gives us a book that explains, in plain terms, the very esoteric subject of differential equations.

The subject should not be esoteric. The limit is encountered in every man's life. Here, we finally see it in action. This is the author's forte. He knows his subject completely.

Hollis has a simple, yet very adventurous plan: Mathematics without appeal to the physical world can not appeal to the average man. In this, he succeeds beyond all expectations.

The Mathematica examples are astounding. Have you ever seen a ticking watch flick, or wondered about the bright moon sailing across the sky, or watched in horror as a raw egg fled from your hand to the floor and wondered: "What happened?" This is the book for you. His explanation of Runge-Kutta is the best I've seen.

The only weakness I perceive is in the section on Laplace transforms. Laplace transforms should require only a mechanical mathematician and some knowledge. Given that Laplace transforms are a fundamental tool, I would have expanded this chapter. The average engineer needs a sound basis. The classroom teacher can decide for himself what his students need.

The last chapters should appeal to those who want to "push the envelope". The equations lay down very neatly and precisely what can and can not be done.

Writing: Very clear. Lot's of examples help the average to excellent student.
Overall: Outstanding. A great learning tool.

Looking forward to the third edition.

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