Numerical Analysis and Scientific Computing

Math 8441 - 8442

Fall, 2013 - Spring 2014

MWF 11:15-12:05

Vincent Hall 313

Instructor for Math 8442: Mitchell Luskin

The goal of this course is to develop the basic mathematical concepts needed to construct and analyze accurate, reliable, and efficient algorithms for the numerical solution of problems in science, mathematics, and technology. The concepts of numerical stability and rate of convergence will be used to develop, compare, and analyze algorithms for both continuum and molecular systems.

Finite element and finite difference methods will be introduced and analyzed for multi-dimensional elliptic partial differential equations. Error estimators and adaptive methods will be developed for problems with singularities. Iterative methods for the solution of the linear systems resulting from the discretization of elliptic partial differential equations will be developed and analyzed.

Methods for ordinary differential equations will be studied with attention given to long-time accuracy, sampling, and multiiple scales. Techniques for error and step size control will be introduced. Methods for molecular dynamics and stochastic differential equations will be developed and analyzed.

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.

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, ordinary differential equations, partial differential equations (Math 5587-8), and numerical analysis (Math 5485-6), or the equivalent. Prospective students should contact the instructor about questions concerning their preparation for this course.

References on reserve for Math 8441 - 8442 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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