Lectures on Differential Geometry with Maple

This text is designed to update the Differential Geometry course by making it more relevant to today's students. It is intended for mathematics students, applied scientists, and engineers who attempt to integrate differential geometry techniques in their work or research.

Autorentext

Mayer Humi is Professor of Mathematics at Worcester Polytechnic University. He holds a Ph.D. in Mathematical Physics and Mathematical Modeling. He is an Associate Editor of the International Journal of Differential Equations and has published over 90 journal papers. His research on the development and application of mathematical methods to atmospheric research and satellites orbits. Other research topics include mathematical physics, celestial mechanics, atmospheric flow, Lie groups, and differential equations.

Inhalt

1. Geometry of Curves in 3D 2. Introduction to Classical Riemannian Geometry 3. Tensor Analysis on Riemann Manifolds 4. Basic Topology and Analysis 5. Differential Manifolds 6. Differentiation on Manifolds 7. Vectors and Bundles 8. Differential Forms 9. Integration on Manifolds in Rn 10. Integration on Manifolds 11. Symmetry and Lie Groups