Vector analysis in Cartesian coordinates; Curvilinear coordinates and transformations to Cartesian, Spherical, and Cylindrical coordinates; line integrals, surface integrals, Green’s theorem, Gauss's divergence theorem, and Stokes’s theorem. Scalar and vector potential.
Review of Series. Linear Algebra; Matrices and linear equations; Matrices and Linear Operators; Determinants, Eigenvalues and eigenvectors.
Complex Numbers and Complex Variable; Representation of complex numbers, DeMoivre’s formula, Powers and roots of complex numbers, Functions of complex variable.