Vector differential calculus. Gradient of scalar field. Divergence and Curl of vector field. Vector integral calculus. Line and surface integrals. Green’s theorem. Divergence theorem of Gauss. Stokes’ theorem. Partial differential equations (PDE). Solution of PDE by separating variables. Solution of PDE by Fourier series. Solution of PDE by Fourier integrals and transforms. Linear algebra. Matrices, determinants, and systems of linear equations. Gauss elimination. Cramer’s rule. Linear dependence. Inverse of a matrix. Vector spaces and subspaces. Rank and nullity. Inner product spaces. Orthonormal bases. Eigenvalues and eigenvectors. Linear transformations. Linear algebra applications.