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Course Outline:

  1. Introduction
    1. Ideas of Error Analysis
    2. Sources of Error
    3. Floating-Point Numbers
    4. Propagation of Errors
  2. Solving Non-linear Equations
    1. Bisection, Regula-Falsi, secant method
    2. Newton's method
    3. Muller's method *
    4. Fixed-point iteration *
    5. Convergence analysis
  3. Curve Fitting, Interpolation and Approximation
    1. Lagrange Polynomials
    2. Divided Difference
    3. Ordinary Difference
    4. Least Squares *
    5. Cubic Splines *
    6. Bezier Curves *
    7. Chebyshev Polynomials *
    8. Economized Power Series *
  4. Numerical Calculus
    1. Derivatives from Difference Tables
    2. Higher-Order Derivatives
    3. Taylor Series
    4. Richardson Extrapolation
    5. Newton-Cotes Integration
    6. The Trapezoid Rule
    7. Simpson's Rule
    8. Romberg Integration
  5. Solving Systems of Equations *
    1. Matrix Issues
    2. Gaussian Elimination
    3. LU Decomposition
  6. Differential Equations *
    1. Euler Methods
    2. Runge-Kutta Methods

(Items marked with * are optional; we will select from these based on the interests of the class and the time available.)

See the course calendar for details concerning exams and assignments.


[HOME] Math 127 (Fall 2011) web pages
Created: 02 Sep 2011
Last modified: Sep 2, 2011 2:25:44 PM
Comments to: dpvc@union.edu
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