Table of Contents

The background: vector calculus; 1. Affine spaces; 2. Curves, functions and derivatives; 3. Vector fields and flows; 4. Volumes and subspaces: exterior algebra; 5. Calculus of forms; 6. Frobenius's theorem; 7. Metrics on affine spaces; 8. Isometrics; 9. Geometry of surfaces; 10. Manifolds; 11. Connections; 12. Lie groups; 13. The tangent and cotangent bundles; 14. Fibre bundles; 15. Connections revisited.

Promotional Information

An introduction to geometrical topics used in applied mathematics and theoretical physics.