Computational Mathematics II

Catalog description

This course in computational mathematics 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. The 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 numerical optimization, numerical differentiation and integration, and computer solutions to differential equations. 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. Code in MATLAB. 2. Solve optimization problems numerically. 3. Differentiate functions numerically. 4. Integrate functions numerically. 5. Find computer solutions to differential equations. 6. Determine numerical solutions to initial-value problems associated to ordinary differential equations. 7. Solve boundary-value problems numerically. 8. Analyze the appropriateness and limitations of each of the above methods, including analyzing error bounds on the results obtained. 9. Effectively communicate results through the project report produced at the conclusion of the semester. View Class Schedule