Difference between revisions of "Math 410: Intro to Numerical Methods"

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(Minimal learning outcomes)
(Minimal learning outcomes)
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#* Cubic spline interpolation
 
#* Cubic spline interpolation
 
# Numerical differentiation
 
# Numerical differentiation
 +
#* Derivation of formulas
 +
#** Backward-difference
 +
#** Forward-difference
 +
#** Centered-difference
 +
#** Error analysis
 
#* Richardson's extrapolation
 
#* Richardson's extrapolation
 
# Numerical integration
 
# Numerical integration
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#* Gaussian quadrature
 
#* Gaussian quadrature
 
#* Multiple integrals
 
#* Multiple integrals
 +
#* Error analysis
 
# Numerical solution of linear systems
 
# Numerical solution of linear systems
 
#* Direct methods
 
#* Direct methods

Revision as of 08:24, 18 February 2010

Catalog Information

Title

Introduction to Numerical Methods.

(Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

Offered

F

Prerequisite

Math 314.

Description

Root finding, interpolation, curve fitting, numerical differentiation and integration, multiple integrals, direct solvers for linear systems, least squares, rational approximations, Fourier and other orthogonal methods.

Desired Learning Outcomes

Prerequisites

Students are required to have had multivariable calculus.

Minimal learning outcomes

  1. Numerical solution of equations of one variable
    • Bisection method
    • Secant method
    • Fixed-point iteration
      • Newton's method
      • Error analysis
    • Polynomial equations
  2. Interpolation
    • Lagrange interpolation
    • Divided-difference methods
    • Hermite interpolation
    • Cubic spline interpolation
  3. Numerical differentiation
    • Derivation of formulas
      • Backward-difference
      • Forward-difference
      • Centered-difference
      • Error analysis
    • Richardson's extrapolation
  4. Numerical integration
    • Newton-Cotes formulas
    • Composite integration
    • Adaptive quadrature
    • Gaussian quadrature
    • Multiple integrals
    • Error analysis
  5. Numerical solution of linear systems
    • Direct methods
      • Gaussian elimination
        • Pivoting strategies
      • Factorization methods
    • Iterative methods
      • Jacobi iteration
      • Gauss-Seidel iteration
      • Relaxation methods

Additional topics

Courses for which this course is prerequisite

Math 410 is the introductory numerical analysis course and is a prerequisite for the other 3 numerical analysis courses: Math 411, 510, and 511. It is also a prerequisite for Math 480.