Computational Mathematics I

Catalog description

This is a graduate-level course in computational mathematics, which is the study of algorithms and methods for computing numerical answers to science and engineering problems. The purpose of this course is to introduce students to the techniques and concepts of modern numerical analysis. In this course, students study algorithms and numerical methods for a variety of basic problems, studying their reliability, efficiency, and computer implementation. This course is designed for graduate students and select advanced undergraduate students in mathematics, computer science, engineering, and sciences. Topics include floating point arithmetic, numerical solutions of equations and systems, eigenvalues and eigenvectors, polynomial and spline interpolation and approximation, and curve fitting. Each numerical method discussed in class is demonstrated through the use of MATLAB, which is user friendly and presents advantages such as: powerful matrix structure, versatile two- and three-dimensional graphing facilities, and a vast number of built-in functions. Typically offered Fall Spring. Course Learning Outcomes 1. Able to Code in MATLAB. 2. Understand the representation of real numbers on computers, the accumulation of roundoff error through a sequence of calculations, and the types of operations that should be avoided in the construction of a numerical algorithm. 3. Find the zeros (roots) of functions numerically (e.g., the bisection method, the method of false position, fixed point iteration schemes, and Newton’s method). 4. Solve linear and nonlinear systems of equations numerically (e.g., Gaussian elimination and iterative techniques for linear systems, and Newton’s method for nonlinear systems). 5. Calculate eigenvalues and eigenvectors. 6. Able to use interpolation and spline functions for solving real-life problems. 7. Represent tabular data through curve fitting. 8. Analyze the appropriateness and limitations of each of the above methods, including determining error bounds on the results obtained. 9. Communicate results through the project report produced at the conclusion of the semester. View Class Schedule