Green's Functions and Linear Differential Equations: Theory, Applications, and Computation: 20 (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)
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Green's Functions and Linear Differential Equations: Theory, Ap...
Book Details
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Author: Prem K. Kythe
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Publisher: CRC Press
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Edition: 1
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Binding: Hardcover
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Pages: 384
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Release Date: 21-01-2011
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ISBN: 9781439840085
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Part Number: 47 black & white illustrations, 9 black
About the Book
Green’s Functions and Linear Differential Equations: Theory, Applications, and Computation by Prem K. Kythe offers a comprehensive exploration of the methods used to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs), particularly through the application of Green’s functions.
Key features include:
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Fundamental Concepts: The book begins with an in-depth examination of the Dirac delta function, providing the theoretical foundation necessary to understand the Green's function method.
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Theoretical and Practical Approach: Following the introduction, Kythe explains how Green’s functions are employed to solve initial and boundary value problems. Several approaches are discussed in the text, including:
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Classical and general variations of parameters
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Wronskian method
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Bernoulli’s separation method
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Integral transform method
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Method of images
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Conformal mapping method
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Interpolation method
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Applications: The text also covers real-world applications of Green’s functions in areas like spherical and surface harmonics.
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Exercises and Examples: The book is filled with worked examples and exercises drawn from various disciplines such as mathematics, applied science, and engineering. These help reinforce the theory and demonstrate its practical use.
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Mathematical Rigor: The text is mathematically rigorous while being accessible enough for readers to appreciate the elegance and utility of the methods presented.
This book is an invaluable resource for advanced students in applied mathematics, engineering, and physics, offering a self-contained, thorough treatment of Green’s functions in solving differential equations.
