A Study of Analytic Functions Based Upon the Theory of Potential Functions: Thesis (Classic Reprint) - Hardcover

Albert Babbitt

9780265548721: A Study of Analytic Functions Based Upon the Theory of Potential Functions: Thesis (Classic Reprint)

Hardcover

ISBN 10: 0265548721 ISBN 13: 9780265548721

Publisher: Forgotten Books, 2018

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Explore the math that links potential theory to analytic functions.

This thesis surveys how potential ideas illuminate the properties, conjugates, and continuations of analytic functions from a physicist’s viewpoint.

This work traces the origin and development of the core concepts, including potential, potential function, and the ways these ideas explain singularities, sources, and the behavior of holomorphic functions. It presents a unique perspective by grounding the definitions of conjugate functions and analytic continuation in physical intuition, while outlining the major theorems and methods that shape the field.

How potential functions relate to the components of attraction and to partial derivatives
Conjugate functions explored from a physics-inspired angle, including conditions for holomorphy
The role of singularities, Green’s theorem, and Poisson’s integral in the analytic theory

Ideal for readers curious about the historical development of potential theory and its connection to analytic functions, with an emphasis on foundations, examples, and the practical methods used to extend and analyze functions. This edition provides a concise, accessible entry into a classic area of mathematical analysis.

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