Memorize and/or know:

Complex number, modulus, complex conjugate, Euler's equation.

How to find the value of a determinant.
How to expand a determinant by the LaPlace method.
How to find the minor, M_ij, of an element of a  determinant
Cramer's method.

How to find the transpose of a matrix
Unit matrix
The 3 rotational matrices for rectangular coordinates.
Method for solving simultaneos equations by matrix methods.
Definitions for orthogonal transformation, orthogonal matrix, eigenvalues,
and eigenvectors.
How to find the characteristic equation, eigenvalues, and eigenvectors
for a  matrix M.
Similarity transformations

Finding dot and cross products of vectors. Determinant expansion of cross product and curl.

Principle of superposition and its application.

How to find a unit vector between two points in space.
Jacobians
parallel axis theorem
center of mass or centroid.
Moment of inertia equation for an extended body.
How to calculate moment of inertia in any coordinate system.

Directional derivative.
How to find a normal vector to any surface.
How to calculate torque, angular velocity and angular momentum.
How to find the gradient, divergence, and curl for any coordinate system.
Meaning of divergence, curl, and circulation in physics (See Boas 6-10, etc.)
Definition for conservative vector field.
The divergence, Gauss, and Stokes Theorems.
How to verify the Stokes and divergenceTheorems.
You should memorize the equations for all of the above in rectangular coordinates.

Average value of a function. (memorize)
Definition of Fourier harmonics.
Fourier's Method.

Orthognal functions. See Boas Chap. 12-6.

Method of separation of variables for solving LaPlace's Equation.
 

To Be Given:

Transformation of rectangular to spherical coordinates.

Equations for the Fourier coefficients  a_n and b_n.

Co-factor of a matrix element a_ij = (-1)^ijM_ij

If you have a question about any other equations or concepts, send e-mail
and I shall post answer here.