Mathematical development, the author of this text observes, comes about through specific, easily understood problems that require difficult solutions and demand the use of new methods. Richard Courant employs this instructive approach in a text that balances the individuality of mathematical objects with the generality of mathematical methods.
Beginning with a discussion of Dirichlet's principle and the boundary-value problem of potential theory, the text proceeds to examinations of conformal mapping on parallel-slit domains and Plateau's problem. Succeeding chapters explore the general problem of Douglas and conformal mapping of multiply connected domains, concluding with a survey of minimal surfaces with free boundaries and unstable minimal surfaces.

About the Author:

The late Richard Courant, headed the Department of Mathematicas at New York University and was Director of the Institute of Mathematical Sciences--which has subsequently renamed the Courant Institute of Mathematical Sciences. His book Mathematical Physics is familiar to every physicist, and his book
Differential and Integral Calculus is acknowledged to be one of the best presentations of the subject written in modern times. Herbert Robbins is New Jersey Professor of Mathematical Statistics at Rutgers University. Ian Stewart is Professor of Mathematics at the University of Warwick, and author of
Nature's Numbers and Does God Play Dice?. He also writes the "Mathematical Recreations" column in Scientific American.

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Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces (Dover Books on Mathematics)

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