Introductory Applications of Partial Differential Equations скачать fb2

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.