FISI 4031: Methods of Mathematical Physics


Vector Calculus. Vector differential calculus: Gradient, divergence, curl. Gradient of a scalar field. Directional Derivative. Divergence and curl of a vector field. Gradient, divergence and curl in curvilinear coordinates. Vector integral calculus: line integrals, Green's theorem on a plane, surface integrals, triple integrals, Gauss' divergence theorem and Stoke's theorem. Linear Algebra: Linear systems of equations, linear independence, definition of a vector space. Matrix algebra, Inverse and determinant of a matrix. Orthogonal, Hermitian and Unitary matrices. Eigenvalue problems and diagonalization of matrices. Differential Equations: First-order ordinary differential equations, separable differential equations, exact differential equations, integrating factors. Wronskian. Second-Order Linear differential equations. Homogeneous differential equations: with constant coefficients, complex roots. Solutions of nonhomogeneous differential equations: by undeterminate coefficients, by variation of parameters, particular solutions.


3 credit hours.


  • MATE 3152: Calculus II