PREREQUISITES: Math 237, Math 238 (formerly 301E), and Math 248
OVERVIEW: Math 448 will revisit many of the themes of Math 248 in greater depth, with more emphasis on mathematical analysis, and with an enlightened eye toward algorithm improvement and refinement of techniques. Specifically, topics will include error propagation and analysis of error, stability and condition, numerical linear algebra (including some iterative methods), approximation methods (e.g., spline interpolation and least-squares techniques), numerical integration techniques, and time-permitting, additional topics such as digital filtering. Unlike Math 248, no class time will be devoted to computer programming per se; that is, students are expected to bring modest programming proficiency to the class. Most, if not all, of the numerical techniques to be studied are of practical utility. Indeed, the instructor used many of the methods in his NASA-related work on the Shuttle Entry Air Data System (SEADS), from which we will draw some motivation. Math 449 (Dr. Sochacki) will extend the notions of 448 to the numerical solution of ordinary and partial differential equations.
INSTRUCTOR:
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Burruss 018 | dpruett@math.jmu.edu |
| 568-6227 | www.math.jmu.edu~/dpruett |
PRIMARY TEXT: Numerical Analysis (6th Ed.) by Burden and Faires, Brooks/Cole 1997.
CLASSIC TEXTS: Elementary Numerical Analysis by Conte and de Boor, McGraw-Hill, 1980. Numerical Recipes by Press, Flannery, Teukolsky, and Vetterling, Cambridge, 1986. Scientific Computing: An Introduction with Parallel Computing, by Golub and Ortega, Academic Press, 1993.
TECHNOLOGY: Some proficiency in a high-level programming language such as Fortran 90 or C is expected. Some familiarity with computer algebra systems (CAS) such as Maple would be helpful.
GRADING:
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| 30% 2 1.5-hour tests, 15% each | Oct. 13, Nov. 22 |
| 10% Homework | Selected assignments to be graded |
| 40% Special assignments | 4-6 during semester |
| 20% Comprehensive final exam | See course schedule |
OUTSIDE HELP: Instructor's office hours: 13:25-14:15MF, 2-4T, 10:10-11W, and by appointment. During scheduled hours, no appointment is necessary; outside of these hours, the favor of an appointment is requested.
MAKE-UPS: No make-up tests will be given. If a test or quiz is missed, for whatever reason, the final exam will be weighted proportionately more heavily.
ATTENDANCE POLICY: Individual success and the success of the course will require faithful on-time attendance.
HONOR POLICY: Students are presumed to have high standards of integrity. To reinforce these standards, the JMU Honor Code will be strictly enforced.