Error analysis convergence and stability. Approximation of functions by polynomials. Numerical quadrature and differentiation. The solution of linear and nonlinear equations and the solution of ordinary differential equations. This course will emphasize the understanding of numerical algorithms and stress applications in the applied sciences, as well as the influence of finite precision and arithmetic on computational results. Note: Students counting credit for MATH 3414 cannot count credit for  CE 2913, CS 3113, ECE 2412, and/or MATH 3413.