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An Introduction to Phase-Integral Methods (Dover Books on Mathematics), by John Heading
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The phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics.
Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself rather than detailed applications. The process, once derived, is shown to be one of essential simplicity that involves merely the application of certain well-defined rules. Starting with a historical survey of the problem and its solutions, subjects include the Stokes phenomenon, one and two transition points, and applications to physical problems. An appendix and bibliography conclude the text.
- Sales Rank: #2375114 in eBooks
- Published on: 2013-06-03
- Released on: 2013-06-03
- Format: Kindle eBook
About the Author
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Most helpful customer reviews
0 of 1 people found the following review helpful.
A good introduction to the WKB method
By Christopher Lioi
The book provides a readable account of the WKB method in applied mathematics. I needed information on the approximation technique for my research, and this book has thusfar fulfilled the need immensely. It provides all the necessary practical details and intuition of the method, but doesn't overload the reader with mathematical rigor and pedantry. This may be unsatisfactory for pure mathematicians, but for the engineer, physicist, or applied mathematician the book has a relatively good balance. My only issue is with the diagrams; the pictures explaining the integration process in the complex plane come with little explanation and may take quite a while for readers to figure out. There are also no plots of the approximate solutions. It would be better if there were some examples qualitatively comparing the approximate solutions with a known exact solution.
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