Difference between revisions of "Math 411: Numerical Methods"
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Revision as of 16:09, 3 April 2013
Contents
Catalog Information
Title
Numerical Methods.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
W
Prerequisite
Description
Iterative solvers for linear systems, eigenvalue, eigenvector approximations, numerical solutions to nonlinear systems, numerical techniques for initial and boundary value problems, elementary solvers for PDEs. [This official course description appears to differ with current standard practice, in that iterative solvers of linear systems are taught in Math 410.]
Desired Learning Outcomes
Prerequisites
The formal prerequisites reflect the fact that incoming students should have basic knowledge of ordinary differential equations and have had a first course in numerical methods. Indirectly, the prerequisites ensure that students have had multivariable calculus.
Minimal learning outcomes
Students should be able to describe, derive, and implement the numerical methods listed below. They should be able to explain the advantages and disadvantages of each method. They should understand error analysis and be able to make practical decisions based on the outcomes of that analysis.
 Numerical solution of initialvalue problems
 Taylor methods
 Euler's method
 RungeKutta methods
 RungeKuttaFehlberg method
 Multistep methods
 Implicit methods
 Extrapolation methods
 Stability
 Stiff differential equations
 Taylor methods
 Numerical solution of boundaryvalue problems
 Shooting methods
 Finitedifference methods
 RayleighRitz method
 Numerical solution of nonlinear systems of equations
 Newton's method
 QuasiNewton methods
 Steepestdescent methods
 Approximation theory
 Leastsquares approximation
 Orthogonal polynomials
 Chebyshev polynomials
 Rational function approximation
 Trigonometric polynomial approximation
 Fast Fourier transforms
 Numerical computation of eigenvalues and eigenvectors
 Power Method
 Partial differential equations
 Finitedifference methods
 For elliptic equations
 For parabolic equations
 For hyperbolic equations
 Finitedifference methods
Textbooks
Possible textbooks for this course include (but are not limited to):
 Richard L. Burden and J. Douglas Faires, Numerical Analysis (9th Edition), Brooks Cole, 2010.
Additional topics
If time permits, students could be given an introduction to finite element methods.
Courses for which this course is prerequisite
None.