Elementary Boundary Value Problems

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CRC Press, Feb 17, 1993 - Mathematics - 264 pages
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This textbook elucidates the role of BVPs as models of scientific phenomena, describes traditional methods of solution and summarizes the ideas that come from the solution techniques, centering on the concept of orthonormal sets of functions as generalizations of the trigonometric functions. To reinforce important concepts, the book contains exercises that range in difficulty from routine applications of the material just covered to extensions of that material.;Emphasizing the unifying nature of the material, this book: constructs physical models for both bounded and unbounded domains using rectangular and other co-ordinate systems; develops methods of characteristics, eigenfunction expansions, and transform procedures using the traditional fourier series, D'Alembert's method , and fourier integral transforms; makes explicit connections with linear algebra, analysis, complex variables, set theory, and topology in response to the need to solve BVP's employing Sturm-Liouville ststems as the primary vehicle; and presents illustrative examples in science and engineering, such as versions of the wave, diffusion equations and Laplace's equations.;Providing fundamental definitions for students with no prior experience in this topic other than differential equations, this text is intended as a resource for upper-level undergraduates in mathematics, physics and engineering, and students on courses on boundary value problems.
 

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Contents

Boundary Value Problems As Models
1
The Method of Characteristics
45
Fourier Series
73
Linear Algebra and SturmLiouville Systems
115
Fourier Transforms
171
A Fourier Series Theorem
215
A Fourier Integral Theorem
225
Proof of Theorems 3 5 2 and 3 5 3
231
On the Zeros of the Bessel Functions
239
Index
245
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