Matrix operations, systems of linear equations, linear spaces and transformations, determinants, eigenvalues and eigenvectors, applications of interest to Engineers including diagonalization of matrices, quadratic forms, orthogonal transformations; introduction to MATLAB with applications from linear algebra.

Introduction to complex numbers, limits, continuity, differentiation of functions of one variable with applications, extreme values, lâ€™Hospitalâ€™s rule, antiderivatives, definite integrals, the Fundamental Theorem of Calculus, the method of substitution.

Techniques of integration, areas and volumes, arclength and surfaces of revolution, applications to physics and engineering, first order differential equations, parametric curves, polar coordinates, sequences and series, vectors and geometry, vector functions, partial differentiation with applications.

Topics include first order ODE's of various types, higher order ODE's and methods of solving them, initial and boundary value problems, applications to mass-spring systems and electrical RLC circuits, Laplace transforms and their use for solving differential equations, systems of linear ODE's, orthogonal functions and Fourier.

Topics covered include a review of orthogonal expansions of functions and Fourier series and transforms, multiple integration with methods of evaluation in different systems of coordinates, vector fields, line integrals, surface and flux integrals, the Green, Gauss and Stokes theorems with applications.

Topics covered include a review of orthogonal expansions of functions and Fourier series, partial differential equations and Fourier series solutions, boundary value problems, the wave, diffusion and Laplace equations, multiple integration with methods of evaluation in different systems of coordinates, vector fields, line integrals, surface and flux integrals, the Green, Gauss and Stokes theorems with applications.

Topics Include: introduction to complex analysis; complex integration; boundary value problems; separation of variables; Fourier series and transform methods of solution for PDE's, applications to electrical engineering.

Variational principles, methods of approximation, basis functions, convergence of approximations, solution of steady state problems, solution of time-dependent problems. Each student will be required to complete two major computational projects.

Finite difference methods, stability analysis for time-dependent problems.

Fourier, Laplace and Hankel transforms with applications to partial differential equations; integral equations; and signal processing and imaging; asymptotic methods with application to integrals and differential equations.