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The Logarithmic Potential: Discontinuous Dirichlet and Neumann Problems

Available Formats:
Softcover ISBN: 978-0-8218-4599-8
Product Code: COLL/6
150 pp
List Price: $42.00 MAA Member Price:$37.80
AMS Member Price: $33.60 Electronic ISBN: 978-1-4704-3156-3 Product Code: COLL/6.E 150 pp List Price:$39.00
MAA Member Price: $35.10 AMS Member Price:$31.20
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List Price: $63.00 MAA Member Price:$56.70
AMS Member Price: $50.40 Click above image for expanded view The Logarithmic Potential: Discontinuous Dirichlet and Neumann Problems Available Formats:  Softcover ISBN: 978-0-8218-4599-8 Product Code: COLL/6 150 pp  List Price:$42.00 MAA Member Price: $37.80 AMS Member Price:$33.60
 Electronic ISBN: 978-1-4704-3156-3 Product Code: COLL/6.E 150 pp
 List Price: $39.00 MAA Member Price:$35.10 AMS Member Price: $31.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$63.00
MAA Member Price: $56.70 AMS Member Price:$50.40
• Book Details

Colloquium Publications
Volume: 61927
MSC: Primary 30; 31;

This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924–1925 at the Rice Institute and at the University of Chicago.

Graduate students and research mathematicians interested in differential equations.

• Chapters
• Chapter 1. Preliminary concepts. Stieltjes integrals and Fourier series
• Chapter 2. Functions harmonic within a circle
• Chapter 3. Necessary and sufficient conditions. The Dirichlet problems for the circle
• Chapter 4. Potentials of a single layer and the Neumann problem
• Chapter 5. General simply connected plane regions and the order of their boundary points
• Chapter 6. Plane regions of finite connectivity
• Chapter 7. Related problems
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Volume: 61927
MSC: Primary 30; 31;

This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924–1925 at the Rice Institute and at the University of Chicago.