The Theory of Potential and Spherical Harmonics / Wolfgang J. Sternberg, Turner L. Smith.

Format:

Book

Author/Creator:

Sternberg, Wolfgang J., Author.

Smith, Turner L., Author.

Series:

Mathematical expositions ; Number 3.

Heritage

Language:

English

Subjects (All):

Potential theory (Mathematics).

Spherical harmonics.

Fisica Matematica.

Physical Description:

1 online resource (xii, 312 pages).

Place of Publication:

Toronto : University of Toronto Press, [2019]

Language Note:

In English.

Summary:

The book is designed chiefly for the use of students and teachers. The research worker will perhaps find some helpful suggestions, as well. The student reading this book is presumed to have a thorough knowledge of differential and integral calculus. In some sections also an acquaintance with the most elementary theorems of the theory of analytic functions and of the theory of linear differential equations is desirable. The text offers a short introduction to vector analysis and a presentation of the Fredholm theory of integral equations. The theory of spherical harmonics is also briefly explained. Consistent use of vector analysis is a characteristic feature of the book. The authors hope that the present text fills a gap, by leading the student reader from the elements of potential theory to the solutions of boundary value problems in a simple and easily understandable way.

Contents:

The Newtonian law of gravity

Concept of potential

The integral theorems of potential theory

Analytic character of the potential : spherical harmonics

Behaviour of the potential at points of the mass

Relation of potential to theory of functions

The boundary value problems of potential theory

The Poisson integral in the plane

The Poisson integral in space

The Fredholm theory in integral equations

General solution of the boundary value problems.

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019)

Includes index.

ISBN:

1-4875-7417-7

OCLC:

1129215492