Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrodinger Equations (Dover Books on Mathematics) [Paperback]

Samuel S. Holland Jr. (Author)

Book Description

Series: Dover Books on Mathematics | Publication Date: June 5, 2007

Numerous examples and exercises highlight this unified treatment of the Hermitian operator theory in its Hilbert space setting. Its simple explanations of difficult subjects make it intuitively appealing to students in applied mathematics, physics, and engineering. It is also a fine reference for professionals. 1990 edition.

Product Details

• Paperback: 576 pages
• Publisher: Dover Publications; Dover Ed edition (June 5, 2007)
• Language: English
• ISBN-10: 0486458016
• ISBN-13: 978-0486458014
• Product Dimensions: 8.5 x 5.8 x 1.1 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #344,416 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

21 of 21 people found the following review helpful:

5.0 out of 5 stars A nice and unsual textbook, August 30, 2007

By 

areader "jguevara7" (Caracas, D.F. Venezuela) - See all my reviews

This review is from: Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrodinger Equations (Dover Books on Mathematics) (Paperback)

This is an interesting book which combines Hilbert spaces, differential equations, and Fourier analysis at very elementary undergraduate level. This textbook may have the best elementary introduction to Schrodinger equation without being a functional analysis or quantum mechanic course. Its applications to Laplace operators and Sturm Liouville problems are very well motivated and developed. This is not a standard textbook, its content and examples are not easily obtained from other sources in the same context. Their early editions were very expensive and hard to find, so this new paperback reedition is welcome.

14 of 14 people found the following review helpful:

5.0 out of 5 stars Perfect for mathematicaal physics courses, December 6, 2007

By 

Francisco Coutinho (Sao Paulo, Sao Paulo Brazil) - See all my reviews
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This review is from: Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrodinger Equations (Dover Books on Mathematics) (Paperback)

This book is for a one year course on functional analysis. It would replace a traditional course course on mathematical physics with advantage.The first two chapters are on ordinary differential equations. They are very good.The third chapter is on Hilbert spaces beggining with the vibrating string , fourier series , etc, thus motivating the last section on Hilbert Spaces.The fourth chapter is on eigenvalues and eigenfunctions of second order differential operators The remaining of the book covers the Schrodinger equation in one dimension , Bessel's Fuctions , Eigenfunctions of the Laplacian and the Fourier transform .The book explain difficult concepts in simple terms. Things like Lebesque integral,Absolutely continuos functions, etc Everything is carefully explained.Let me quote this passage on page 419: "The elements of this Hilbert Space are functions of two variables.The Hilbert spaces we considered in earlier chapters consisted in functions of one variable. Does this confuses us? Not us!"In fact the book is almost perfect

2 of 2 people found the following review helpful:

5.0 out of 5 stars Insightful, March 2, 2010

By 

Ken Braithwaite (inkster, MI USA) - See all my reviews
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This review is from: Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrodinger Equations (Dover Books on Mathematics) (Paperback)

This is an outstanding book. It skims the theory -- he is quite explicit about this -- but shows well how the methods work. You could call this "why separation of variable works". If you read more in functional analysis this book will serve as great mathematical "motivation". All his explanations are very clear, and there are a lot of examples.