Tensor Calculus / John Lighton Synge, Alfred Schild.

Format:

Book

Author/Creator:

Lighton Synge, John, Author.

Schild, Alfred, Author.

Series:

Mathematical expositions ; Number 5.

Heritage

Language:

English

Subjects (All):

Calculus of tensors.

Genre:

Electronic books.

Physical Description:

1 online resource (335 pages).

Place of Publication:

Toronto : University of Toronto Press, [2020]

Language Note:

In English.

Summary:

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.

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

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 05. Mai 2020)

ISBN:

1-4875-8405-9

OCLC:

1153507363