Instructor: Douglas N. Arnold
Contact info: 332 McAllister Building, telephone: 865-0246, email: dna@psu.edu
Office hours: Monday 10:00-11:00, Thursday 10:30-11:30 and by appointment
WWW Page: http://www.math.psu.edu/dna/597.00-01
Homework: (fall)
Lecture schedule: fall and spring
About the course: This course is a two-semester graduate level introduction to numerical analysis. The primary subject matter is the design and performance of algorithms to solve problems in mathematial analysis and algebra: the mathematical theory behind scientific and engineering computing. The course will cover the classical fundamental topics in numerical analysis: approximation, numerical integration, numerical linear algebra, solution of nonlinear algebraic systems, optimization, and solution of ordinary and partial differential equations. The viewpoint will be modern, with connections made to the main currents of contemporary research in numerical mathematics. See the syllabus for detailed contents. | |
This course was introduced a few years ago in conjunction with the Applied Math Option for the mathematics Ph.D. degree and also serves to prepare students for the numerical analysis qualifying exam, which is required by that option. This is the second offering of the course (I taught the first offering in 1998-99). | Motivation for studying numerical analysis: The first time this offshore platform was installed, it crashed to the sea bottom causing a seismic event measuring 3.0 on the Richter scale and costing $700,000,000. The cause: flawed algorithms for the numerical solution of the relevant partial differential equations. For more information see here. |
References: During the first offering of the course I developed a set of notes which will be the primary reference for the course. I intend to extend and polish these during the year, and will provide updates as they become available. For reference I recommend the classic Analysis of Numerical Methods, by Eugene Isaacson and Herbert Bishop Keller; Dover Publications 1994 and Introduction to Numerical Analysis, by J. Stoer and R. Bulirsch; Springer-Verlag 1980. ISBN 0-387-90420-4.
Exams and homework: There will homework sets every few weeks, a midterm, and a final exam.