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Description

Basic computational methods for interpolation, least squares, approximation, numerical quadrature, numerical solution of nonlinear equations, systems of linear equations, and initial value problems for ordinary differential equations. Emphasis on the methods and their computational properties rather on their analytic aspects. Will use MATLAB.

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241); and 1 course with a minimum grade of C- from (CMSC106, CMSC131); and minimum grade of C- in MATH246.

Level of Rigor

Standard

Sample Textbooks

  • Numerical Analysis by R. Burden, J. Faires, A. Burden
  • Numerical Computing with Matlab, by Cleve B. Moler

Applications

Computer Science, Economics, Business, Engineering, Physics, Astronomy

If you like this course, you might also consider the following courses:

Math 420, Math 416, Stat 430.

Additional Notes

  • Duplicate credit with AMSC466 and CMSC466; cross-listed with CMSC460
  • Students interested in grad school in Applied Math should consider this course
  • Students interested in grad school in Statistics should consider this course

Topics

  • Computer Arithmetic and Errors
  • Machine arithmetic
  • Error analysis
  • Stability and conditioning
  • Solving linear systems of equations
  • Gaussian elimination
  • well-conditioning vs. ill-conditioning, matrix and vector norms
  • Software for Gaussian elimination
  • Interpolation
  • Polynomial interpolation
  • Piecewise polynomial interpolation
  • Spline interpolation
  • Software for interpolation
  • Numerical Integration
  • Elementary integration formulas (midpoint, trapezoidal rules, etc.)
  • Gaussian quadrature
  • Adaptive quadrature
  • Software for adaptive integration
  • Solution of nonlinear systems of equations
  • Bisection method, secant method, Newton's method
  • Methods for systems of equations
  • Software for solving nonlinear equations
  • Numerical solution of ordinary differential equations
  • Stability and stiffness
  • Basic numerical methods
  • Stepsize control
  • Methods for stiff systems
  • Software for solving initial value problems
  • Linear least squares problems
  • Data fitting and least squares
  • QR factorization
  • Software for least squares problems 
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