Introductory Applications of Partial Differential Equations: With Emphasis on Wave Propagation and Diffusion

John Wiley & Sons, Apr 17, 1995 - Mathematics - 471 pages
INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

With Emphasis on Wave Propagation and Diffusion

This is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematics and physics. Rather than presenting the mathematics in isolation and out of context, problems in this text are framed to show how partial differential equations can be used to obtain specific information about the physical system being analyzed.

Designed for upper-level students, professionals and researchers in engineering, applied mathematics, physics, and optics, Professor Lamb's text is lucid in its presentation and comprehensive in its coverage of all the important topic areas, including:

• One-Dimensional Problems
• The Laplace Transform Method
• Two and Three Dimensions
• Green's Functions
• Spherical Geometry
• Fourier Transform Methods
• Perturbation Methods
• Generalizations and First Order Equations

In addition, this text includes a supplementary chapter of selected topics and handy appendices that review Fourier Series, Laplace Transform, Sturm-Liouville Equations, Bessel Functions, and Legendre Polynomials.

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Contents

 Laplace Transform Method 60 Two and Three Dimensions 85 Greens Functions 142 Spherical Geometry 226 Fourier Transform Methods 255 One Two and Three Dimensions 291 Perturbation Methods 297 Generalizations and First Order Equations 317
 Selected Topics 352 Appendix A Fourier Series 391 Appendix B Laplace Transform 410 SturmLiouville Equations 426 Bessel Functions 436 Appendix E Legendre Polynomials 450 Appendix F Tables of Sums and Integral Transforms 462 Copyright

References to this book

 Applied Partial Differential Equations: An IntroductionAlan JeffreyLimited preview - 2003
 Partial Differential EquationsHarold LevineNo preview available
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