Error analysis; numerical methods for interpolation, approximation, integration, and solution of non-linear equations and differential equations. Computer programs written and analyzed. (Offered as needed.)

CIS 181 Computer Programming I and MATH 211 Calculus III

Lamarr C. Widmer, Ph.D., Associate Professor of Mathematics

Students majoring in mathematics, computer science, or engineering.

The student will acquire a knowledge of standard algorithms for the approximate solution of algebra and calculus problems. This will include an understanding of the motivation and underlying concepts of these methods as well as their implementation by means of various computational technologies. We also intend to examine the various factors which influence the performance of these programs and develop an ability to judge and, when necessary, improve their reliability in specific applications.

1. Taylor polynomials
2. Rootfinding: bisection, Newton, secant and fixed point iteration methods
3. Polynomial interpolation: Lagrange and Newton versions, interpolation error, natural cubic spline
4. Function approximation: best approximation problem, near minimax approximation
5. Numerical integration: Trapezoidal, Simpson and Gaussian methods
6. Numerical Differentiation: differentiation of interpolating polynomials, method of undetermined coefficients
7. Least squares curve fitting