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

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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

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About the author (1995)

G. L. LAMB, Jr., is Professor of Mathematics and Optical Sciences at the University of Arizona.

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