[Vectorial Mechanics:] vector functions of time; laws of mechanics in vector form; derivative of dot and cross products; angular momentum and torque in vector form; line integrals and work; conservation of energy and potential function; applications to planetary dynamics.
[Vector Calculus:] scalar and vector fields; contour maps, directional derivative and gradient vector of scalar fields; divergence and curl of vector field; applications in electromagnetism and fluid mechanics; vector identities; surface and volume integrals; Gauss's and Stoke's theorems.
[Tensor Algebra and Calculus:] Review of matrix algebra introducing suffix notation; transformation properties of tensors; symmetric and anti-symmetric tensors, with special reference to examples from mechanics and electromagnetics; the Levi-Civita tensor.