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

View this Free Online Material at the source:

Introduction to Tensor Calculus and Continuum Mechanics