Differential Geometry And Tensors

Differential Geometry And Tensors
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Differential Geometry And Tensors

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Publisher: IK International
ISBN: 9789380026589
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Differential Geometry And Tensors by K.K. Dube
Book Summary:

The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self-contained and divided in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors.

Section A deals with : theory of curves, envelopes and developables; curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature; fundamental equations of surface theory; and, geodesics.

Section B deals with : tensor algebra; tensor calculus; Christoffel symbols and their properties; Riemann symbols and Einstein space, and their properties; physical components of contravariant and covariant vectors; geodesics and parallelism of vectors; and, differentiable manifolds, charts, atlases.


Audience of the Book :
This book has been systematically organized in a easy way to read. This book will surve as suitable text cum reference book for the students of M.Sc. and B.Sc. honours from various universities.
 
Key Features:

The main features of the book are as follows:

1. Theory of curves, envelopes and developables.

2.Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature.

3.Fundamental equations of surface theory.

4.Geodesics.


Table of Contents:

Section A

1.Differential Geometry: Vector Notations

2.Theory of Curves in Space

3.Envelopes and Developables

4.Curves on Surfaces and Fundamental Magnitudes

5.Curvature of Surfaces and Lines of Curvature: Local Non-Intrinsic Properties of Surface

6.Fundamental Equations of Surface Theory

7.Geodesics

Section B:

1.Tensor: Introduction

2.Tensor Algebra

3.Tensor Calculus

4.Christoffel Symbols, Covariant Differentiation, and their Properties

5.Riemann Symbols

6.Geodesics, Riemannian Coordinates, Geodesic Coordinates and Parallelism of Vectors

7.Differentiable Manifolds and Riemannian Manifolds