Differential Geometry / / Erwin Kreyszig.

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Kreyszig, Erwin,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2019]; ©1959
• Year of Publication: 2019
• Language: English
• Series: Heritage
• Physical Description: 1 online resource (394 p.)

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.

Table of 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