Kernel Functions and Elliptic Differential Equations in Mathematical Physics (Dover Books on Mathematics) by Stefan Bergman (PDF)

Description

This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.The two-part treatment begins with a survey of boundary value problems occurring in certain branches of theoretical physics. It introduces fundamental solutions in a heuristic way and examines their physical significance. Many concepts can be unified by concentrating upon these particular kernels, and the text explains the common mathematical background of widely varying theories, such as those of heat conduction, hydrodynamics, electrostatics, magnetostatics, and elasticity. In addition to its intrinsic interest, this material provides illustrations and exact mathematical formulation of the problems and the methods. The second part is confined to a rather special type of partial differential equation, which is dealt with in the greatest detail so that students can make applications and generalizations to similar problems.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A very nice and rigorous work dating to the 1950’s by two researchers whose education reflects the applied ethos of New York University.The notations for vector quantities are a bit dated, for example, div instead of del dot (del .), and curl instead of del cross (del X). But that is quite all right.For a book based on applications, one hopes to see solid applications. However, the book here is oriented toward a theoretical approach toward applications that arise from problems in Classical Physics and Engineering. It does not lend to effective methods of attack in finding solution to partial differential equations (P.D.E.’s)albeit the theoretical treatment and analyses of such elliptic P.D.E.’s are quite elegant.All in all, a very nice and rigorous treatment of elliptic P.D.E.’s with a tilt toward solving problems arising in Classical Physics and Engineering.

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