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

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Sternberg, Wolfgang J.,; Smith, Turner L.,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2019]; ©1944
• Year of Publication: 2019
• Language: English
• Series: Heritage
• Physical Description: 1 online resource (324 p.)

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.

Table of Contents

Frontmatter -- PREFACE -- CONTENTS -- INTRODUCTION -- I. THE NEWTONIAN LAW OF GRAVITY -- II. CONCEPT OF POTENTIAL -- III. THE INTEGRAL THEOREMS OF POTENTIAL . THEORY -- IV. ANALYTIC CHARACTER OF THE POTENTI..L. SPHERICAL HARMONICS -- V. BEHAVIOUR OF THE POTENTIAL AT POINTS OF THE MASS -- VI. RELATION OF POTENTIAL TO THEORY OF FUNCTIONS -- VII. THE BOUNDARY VALUE PROBLEMS OF POTENTIAL THEORY -- VIII. THE POISSON INTEGRAL IN THE PLANE -- IX. THE' POISSON INTEGRAL IN SPACE -- X. THE FREDHOLM THEORY OF INTEGRAL EQUATIONS -- XI. GENERAL SOLUTION OF THE BOUNDARY VALUE PROBLEMS -- INDEX