Difference between revisions of "Math 411: Numerical Methods"

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=== Minimal learning outcomes ===
 
=== Minimal learning outcomes ===
 +
 +
[Draft of 12/31/2009]
  
 
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<div style="-moz-column-count:2; column-count:2;">
  
# Initial Value Problems
+
# Numerical solution of initial-value problems
# Boundary Value Problems
+
#* Euler's method
Nonlinear
+
#* Runge-Kutta methods
#  Approximation Theory
+
#** Runge-Kutta-Fehlberg method
#* Least Squares approximation
+
#* Multi-step methods
#*  
+
#* Extrapolation methods
Eigenvalue Problems
+
#* Stability
 +
#* Stiff differential equations
 +
# Numerical solution of boundary-value problems
 +
Numerical solution of nonlinear systems of equations
 +
#  Approximation theory
 +
#* Least-squares approximation
 +
#* Orthogonal polynomials
 +
#** Chebyshev polynomials
 +
#* Rational function approximation
 +
#* Trigonometric polynomial approximation
 +
#* Fast Fourier transforms
 +
Numerical computation of eigenvalues and eigenvectors
 
#*  Power Method
 
#*  Power Method
#  Partial Differential Equations
+
#  Partial differential equations
  
 
</div>
 
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Revision as of 14:08, 31 December 2009

Catalog Information

Title

Numerical Methods.

(Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

Offered

W

Prerequisite

Math 334, 410.

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.

Desired Learning Outcomes

Prerequisites

Minimal learning outcomes

[Draft of 12/31/2009]

  1. Numerical solution of initial-value problems
    • Euler's method
    • Runge-Kutta methods
      • Runge-Kutta-Fehlberg method
    • Multi-step methods
    • Extrapolation methods
    • Stability
    • Stiff differential equations
  2. Numerical solution of boundary-value problems
  3. Numerical solution of nonlinear systems of equations
  4. Approximation theory
    • Least-squares approximation
    • Orthogonal polynomials
      • Chebyshev polynomials
    • Rational function approximation
    • Trigonometric polynomial approximation
    • Fast Fourier transforms
  5. Numerical computation of eigenvalues and eigenvectors
    • Power Method
  6. Partial differential equations

Additional topics

Courses for which this course is prerequisite