Topics and Goals: Numerical analysis introduces students to the necessity to develop methods for problem solving that are both robust and efficient. We seek solutions to problems that do not necessarily have exact solutions. Thus our solutions are approximations and we focus on developing the error analysis on these approximate solutions. The two parallel themes are (1) how to estimate the solution and (2) how close is our estimate to the true but unknown solution.

Students will use existing mathematical software during the course. In particular, there will be some homework assignments and test problems which will require Maple.

Topics usually covered include (1) Solutions of Equations in One Variable using the bisection algorithm, the fixed point method, Newton's method, and the secant method, (2) Interpolation and Polynomial Approximations using Lagrange polynomials, Hermite polynomials, Chebyshev polynomials, Neville's method, Newton's divided differences, and Pade' approximations, and (3) Numerical Differentiation and Integration including the trapezoid rule, Romberg integration, and an adaptive Simpson's rule.

Relationship to other courses: Math 430 continues the study of calculus. The students will see many uses of the theorems from Calculus, e.g., Taylor's Theorem and the Intermediate Value Theorem.