Course Coordinator: 
Eliot Fried
Vector and tensor calculus

A geometrically oriented introduction to the calculus of vector and tensor fields on three-dimensional Euclidean point space, with applications to the kinematics of point masses, rigid bodies, and deformable bodies. Aside from conventional approaches based on working with Cartesian and curvilinear components, coordinate-free treatments of differentiation and integration will be presented. Connections with the classical differential geometry of curves and surfaces in three-dimensional Euclidean point space will also be established and discussed.

Detailed Syllabus: 

1. Euclidean point and vector spaces

2. Geometry and algebra of vectors and tensors

3. Cartesian and curvilinear bases

4. Vector and tensor fields

5. Differentiation and integration

6. Covariant, contravariant, and physical components

7. Basis-free descriptions

8. Kinematics of point masses

9. Kinematics of rigid bodies

10. Kinematics of deformable bodies

Course Type: 
weekly problem sets, a midterm examination, and a final examination
Text Book: 
none, working from personal notes
Reference Book: 
Prior Knowledge: 

multivariate calculus and linear (or, alternatively, matrix) algebra