Introduction To Tensor Calculus & Continum Mechanics by J. H. Heinbockel
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About this book :-
Introduction To Tensor Calculus & Continum Mechanics written by
J.H. Heinbockel
The purpose of preparing these notes is to condense into an introductory text the basic definitions and techniques arising in tensor calculus, differential geometry and continuum mechanics. In particular, the material is presented to (i) develop a physical understanding of the mathematical concepts associated with tensor calculus and (ii) develop the basic equations of tensor calculus, differential geometry and continuum mechanics which arise in engineering applications. From these basic equations one can go on to develop more sophisticated models of applied mathematics. The material is presented in an informal manner and uses mathematics which minimizes excessive formalism.
The material has been divided into two parts. The first part deals with an introduction to tensor calculus and dierential geometry which covers such things as the indicial notation, tensor algebra, covariant dierentiation, dual tensors, bilinear and multilinear forms, special tensors, the Riemann Christoel tensor, space curves, surface curves, curvature and fundamental quadratic forms. The second part emphasizes the application of tensor algebra and calculus to a wide variety of applied areas from engineering and physics. The selected applications are from the areas of dynamics, elasticity, fluids and electromag netic theory. The continuum mechanics portion focuses on an introduction of the basic concepts from linear elasticity and fluids.
Book Detail :-
Title: Introduction To Tensor Calculus & Continuum Mechanics
Edition:
Author(s): J.H. Heinbockel
Publisher: Trafford Publishing
Series:
Year: 2001
Pages: 374
Type: PDF
Language: English
ISBN: 1553691334,9781553691334
Country: US
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About Author :-
The author J.H. Heinbockel is PhD, Emeritus Professor of Mathematics at Department of Mathematics and Statistics, Old Dominion University.
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Book Contents :-
Introduction To Tensor Calculus & Continum Mechanics written by
J.H. Heinbockel
cover the following topics.
PART-1 INTRODUCTION TO TENSOR CALCULUS
1.1 INDEX NOTATION
1.2 TENSOR CONCEPTS AND TRANSFORMATIONS
1.3 SPECIAL TENSORS
1.4 DERIVATIVE OF A TENSOR
1.5 DIFFERENTIAL GEOMETRY AND RELATIVITY
PART-2 INTRODUCTION TO CONTINUUM MECHANICS
2.1 TENSOR NOTATION FOR VECTOR QUANTITIES
2.2 DYNAMICS
2.3 BASIC EQUATIONS OF CONTINUUM MECHANICS
2.4 CONTINUUM MECHANICS (SOLIDS)
2.5 CONTINUUM MECHANICS (FLUIDS)
2.6 ELECTRIC AND MAGNETIC FIELDS
BIBLIOGRAPHY
APPENDIX A UNITS OF MEASUREMENT
APPENDIX B CHRISTOFFEL SYMBOLS OF SECOND KIND
APPENDIX C VECTOR IDENTITIES
INDEX
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