Introduction to Tensor Calculus and Continuum Mechanics

Written by: John H. Heinbockel (Old Dominion University)

This calculus textbook could be used as part of an introductory 2-semester text on tensor calculus, differential geometry and continuum mechanics suitable for advanced undergraduates or graduate students studying applied mathematics, engineering and physics. John H. Heinbockel, Professor Emeritus, Department of Mathematics and Statistics, Old Dominion University is offering an early version of this textbook, which includes approximately 80% of the material in the final version which is available for purchase.

You can download a single, zipped file of the material or view it online in a number of PDF files.

Table of Contents

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
Appendix A: Units Of Measurement
Appendix B: Christoffel Symbols Of Second Kind
Appendix C: Vector Identities

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Introduction to Tensor Calculus and Continuum Mechanics

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