Singular Perturbation Theory: Mathematical and Analytical Techniques with Applications to Engineering [Hardcover]

R.S. Johnson (Author)

Book Description

ISBN-10: 0387232001 | ISBN-13: 978-0387232003 | Publication Date: December 15, 2004 | Edition: 1

The theory of singular perturbations has evolved as a response to the need to find approximate solutions (in an analytical form) to complex problems. Typically, such problems are expressed in terms of differential equations which contain at least one small parameter, and they can arise in many fields: fluid mechanics, particle physics, and combustion processes, to name but three.

Editorial Reviews

Review

From the reviews:

"It is based on material taught by the author … and is very much a textbook, filled with a very large number of worked examples and end-of-chapter exercises, with answers and hints for the latter in the back of the book. … Appropriate references are cited throughout the book. … It would be an excellent text for an applied mathematics course on singular perturbations. Its accessibility and clarity would make it equally valuable to someone not familiar with the subject … ." (Stanley A. Berger, AIAA Journal, Vol. 44 (4), 2006)

From the Back Cover

Many areas of science and engineering produce difficult mathematical problems , i.e., problems that cannot be solved in any conventional sense. In many cases, against all the apparent odds, it is possible to construct systematic approximations that lead to useful solutions. The most powerful of these approximation techniques is singular perturbation theory.

Singular Perturbation Theory introduces all the background ideas to this subject, designed for those with only the most superficial familiarity with university-level mathematics. The methods are developed through worked examples and set exercises (with answers); the latter part of the book is devoted to applications drawn from: mechanics, physics, semi- and superconductor theory, fluid mechanics, thermal processes, chemical and biochemical reactions. In a novel approach, these are grouped together so that the reader with particular interests can readily access them.

This book is based on material that has been taught, mainly by the author, to MSc and research students in applied mathematics and engineering mathematics at the University of Newcastle upon Tyne over the last thirty years. The aim of this text is to make all the material readily accessible to the reader who wishes to learn and use the ideas to help with research problems and who does not have a strong mathematical background.

Product Details

• Hardcover: 308 pages
• Publisher: Springer; 1 edition (December 15, 2004)
• Language: English
• ISBN-10: 0387232001
• ISBN-13: 978-0387232003
• Product Dimensions: 9.5 x 6.1 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #511,446 in Books (See Top 100 in Books)

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