Tensor Calculus / / John Lighton Synge, Alfred Schild.

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Lighton Synge, John,; Schild, Alfred,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2020]; ©1949
• Year of Publication: 2020
• Language: English
• Series: Heritage
• Physical Description: 1 online resource (336 p.)

A mathematician unacquainted with tensor calculus is at a serious disadvantage in several fields of pure and applied mathematics. He is cut off from the study of Riemannian geometry and the general theory of relativity. Even in Euclidean geometry and Newtonian mechanics (particularly the mechanics of continua) he is compelled to work in notations which lack the compactness of tensor calculus. This book is intended as a general brief introduction to tensor calculus. As treatments of tensor calculus directed towards relativity are comparatively numerous, relativity has been excluded almost completely, and the aplications to classical mathematical physics emphasized. However, by using a metric which may be indefinite, an adequate basis for applications to relativity has been given.

Table of Contents

Frontmatter -- PREFACE -- CONTENTS -- I. SPACES AND TENSORS -- II. BASIC OPERATIONS IN RIEMANNIAN SPACE -- III. CURVATURE OF SPACE -- IV. SPECIAL TYPES OF SPACE -- V. APPLICATIONS TO CLASSICAL DYNAMICS -- VI. APPLICATIONS TO HYDRODYNAMICS, ELASTICITY, AND ELECTROMAGNETIC RADIATION -- CHAPTER VII. RELATIVE TENSORS, IDEAS OF VOLUME, GREEN-STOKES THEOREMS -- CHAPTER VIII. NON-RIEMANNIAN SPACES -- Appendix A. Reduction of a Quadratic Form -- Appendix B. Multiple Integration -- BIBLIOGRAPHY -- INDEX