Tensor Calculus Heinbockel The material. Each section includes many illustrative worked examples. At the end of each. Many new ideas. The purpose of preparing these notes is to condense into an introductory text the basic.
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Francisco Ulisses da Cunha Barros flag Denunciar. The material presented is suitable for a two semester course in applied mathematics and is flexible enough to be presented to either upper level undergraduate or beginning graduate students majoring in applied mathematics, engineering or physics.
The presentation assumes the students have some knowledge from the areas of matrix theory, linear algebra and advanced calculus. Each section includes many illustrative worked examples. Many new ideas are presented in the exercises and so the students should be encouraged to read all the exercises. 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 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. The Appendix C is a summary of useful vector identities. All rights reserved. An n- dimensional vector field is described by a one-to-one correspondence between n-numbers and a point.
Let us generalize these concepts by assigning n-squared numbers to a single point or n-cubed numbers to a single point. When these numbers obey certain transformation laws they become examples of tensor fields. In general, scalar fields are referred to as tensor fields of rank or order zero whereas vector fields are called tensor fields of rank or order one.
Closely associated with tensor calculus is the indicial or index notation. In section 1 the indicial notation is defined and illustrated. We also define and investigate scalar, vector and tensor fields when they are subjected to various coordinate transformations. It turns out that tensors have certain properties which are independent of the coordinate system used to describe the tensor. Because of these useful properties, we can use tensors to represent various fundamental laws occurring in physics, engineering, science and mathematics.
These representations are extremely useful as they are independent of the coordinate systems considered. This notation focuses attention only on the components of the vectors and employs a dummy subscript whose range over the integers is specified. The dummy subscript i can have any of the integer values 1, 2 or 3. The subscript i is a dummy subscript and may be replaced by another letter, say p, so long as one specifies the integer values that this dummy subscript can have.
Note that many.
Heinbockel J.H. Introduction to Tensor Calculus and Continuum Mechanics
No eBook available Amazon. There are four Appendices. The Appendix B contains a listing of Christoffel symbols of the second kind associated with various coordinate systems. The Appendix C is a summary of use ful vector identities. The Appendix D contains solutions to selected exercises. The text has numerous illustrative worked examples and over exercises.
Heinbockel J. Trafford Publishing, Introduction to Tensor Calculus and Continuum Mechanics is an advanced College level mathematics text. The first part of the text introduces basic concepts, notations and operations associated with the subject area of tensor calculus.
Tensor Calculus (Heinbockel 373). - Index of
For full document please download. The presentation assumes the students have some knowledge from the areas of matrix theory, linear algebra and advanced calculus. Each section includes many illustrative worked examples. Many new ideas are presented in the exercises and so the students should be encouraged to read all the exercises. 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.