Vector and Tensor Calculus

Course Description

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.

Course Contents

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, contraviant, and physical components

7. Basis-free descriptions

8. Kinematics of point masses

9. Kinematics of rigid bodies

10. Kinematics of deformable bodies


weekly problem sets, a midterm examination, and a final examination

Prerequisites or Prior Knowledge

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


none, working from personal notes


Alternate years course, odd years alternates with A112

Research Specialties