Differential Geometry / Erwin Kreyszig.

Format:

Book

Author/Creator:

Kreyszig, Erwin, author.

Series:

Mathematical expositions ; Number 11.

Heritage

Language:

English

Subjects (All):

Geometry, Differential.

Genre:

Electronic books.

Physical Description:

1 online resource (377 pages) : illustrations.

Place of Publication:

Toronto : University of Toronto Press, [2019]

Language Note:

In English.

Summary:

This book is intended to meet the need for a text introducing advanced students in mathematics, physics, and engineering to the field of differential geometry. It is self-contained, requiring only a knowledge of the calculus. The material is presented in a simple and understandable but rigorous manner, accompanied by many examples which illustrate the ideas, methods, and results. The use of tensors is explained in detail, not omitting little formal tricks which are useful in their applications. Though never formalistic, it provides an introduction to Riemannian geometry. The theory of curves and surfaces in three-dimensional Euclidean space is presented in a modern way, and applied to various classes of curves and surfaces which are of practical interest in mathematics and its applications to physical, cartographical, and engineering problems. Considerable space is given to explaining and illustrating basic concepts such as curve, arc length, surface, fundamental forms; covariant and contravariant vectors; covariant, contravariant and mixed tensors, etc. Interesting problems are included and complete solutions are given at the end of the book, together with a list of the more important formulae. No pains have been spared in constructing suitable figures.

Contents:

Frontmatter

PREFACE

CONTENTS

CHAPTER I. PRELIMINARIES

CHAPTER II. THEORY OF CURVES

CHAPTER III. CONCEPT OF A SURFACE. FIRST FUNDAMENTAL FORM. FOUNDATIONS OF TENSOR CALCULUS

CHAPTER IV. SECOND FUNDAMENTAL FORM. GAUSSIAN AND MEAN CURVATURE OF A SURFACE

CHAPTER V. GEODESIC CURVATURE AND GEODESICS

CHAPTER VI. MAPPINGS

CHAPTER VII. ABSOLUTE DIFFERENTIATION AND PARALLEL DISPLACEMENT

CHAPTER VIII. SPECIAL SURFACES

SUPPLEMENTARY PROBLEMS

ANSWERS TO PROBLEMS

ANSWERS TO ODD-NUMBERED SUPPLEMENTARY PROBLEMS

COLLECTION OF FORMULAE

BIBLIOGRAPHY

INDEX

Notes:

Includes bibliographical references and index.

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

ISBN:

9781487591069

1487591063

9781487589455

148758945X

OCLC:

1091658838