Numerical Analysis and Scientific Computing

Math 8441-8442

Fall, 2007 - Spring, 2008

MWF 11:15-12:05

Vincent Hall 209

Instructor: Mitchell Luskin

The goal of this year course is to teach the basic mathematical concepts needed to develop accurate, reliable, and efficient algorithms for the numerical solution of problems in science, mathematics, and technology. The course will use the concepts of numerical stability and rate of convergence to develop and analyze algorithms for several classes of problems.

Methods for ordinary differential equations will be studied with attention given to long-time stability, rate of convergence, and multiple scales. Techniques for error and step size control will be introduced.

Finite element and finite difference methods will be introduced and analyzed for multi-dimensional elliptic partial differential equations. We will then learn about direct and iterative methods for the solution of the linear systems resulting from the discretization of elliptic partial differential equations.

The final part of the course will develop and analyze methods for the numerical solution of parabolic and hyperbolic partial differential equations. Techniques for time discretization developed for ordinary differential equations will be applied to partial differential equations, and techniques for the solution of linear and nonlinear equations will be developed to solve implicit methods.

Homework will be given to develop analytic and computational skills. The computational assignments will utilize MATLAB.

The prerequisites for this course are undergraduate courses in linear algebra, differential equations, and numerical analysis, or the equivalent.

References on reserve for Math 8441-2 can be found in the Mathematics Library in 310 Vincent Hall.

For more information or questions, please contact

Mitchell Luskin
e-mail: luskin@math.umn.edu
Phone: 625-6565
Vincent Hall 330

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