Marcelo Epstein is currently a Professor of Mechanical Engineering at the University of Calgary, Canada. His main research has centered around the various aspects of modern continuum mechanics and its applications. A secondary related area of interest is biomechanics. He is a Fellow of the American Academy of Mechanics, recipient of the Cancam prize and University Professor of Rational Mechanics. He is also adjunct Professor in the Faculties of Humanities and Kinesiology at the University of Calgary.
Part I. Motivation and Background: 1. The case for differential geometry
2. Vector and affine spaces
3. Tensor algebras and multivectors
Part II. Differential Geometry: 4. Differentiable manifolds
5. Lie derivatives, lie groups, lie algebras
6. Integration and fluxes
Part III. Further Topics: 7. Fibre bundles
8. Inhomogeneity theory
9. Connection, curvature, torsion
Appendix A. A primer in continuum mechanics.
