MATH 570 NUMERICAL METHODS I

Course Syllabus

  1. Computers, Errors and Algorithms
    1. Introduction
    2. Numerical Methods
    3. Digital Devices and Errors
    4. Representation of Real Numbers in a Computer
    5. Errors in Fixed Precision Arithmetic
    6. Reducing and Avoiding Roundoff Error
    7. Errors, Accuracy and Tests for Closeness
    8. Iterative Algorithms
    9. Numerical Methods for Finding Roots and Solving Equations
      1. Solving Equations and Finding Roots
      2. Methods for Finding roots
      3. Convergence Rate and Accuracy
      4. Finding Roots of Real Polynomials
  2. Solving Linear Systems Exactly Using Direct Methods
    1. Basic Properties of Matrices
    2. The LU-Factorization Algorithm
    3. Gauss-Jordan Elimination
    4. Determinants
    5. Cramer's Rule
  3. Solving Linear and Nonlinear Systems Using Fixed Precision Arithmetic
    1. Minimizing Round-off
    2. Ill-conditioned Coefficient Matrices
    3. Assessing and Improving the Accuracy of a Solution
    4. Solving AX=B on a Computer
    5. Iterative Methods for Solving Linear Systems
    6. Solving Nonlinear Systems
  4. Curve Fitting and Function Approximation
    1. Fitting Curves to Discrete Data (Computer Program)
    2. Fitting Two Parameter Curves to Monotone Convex Data (Computer Program)
    3. Fitting Curves that are Linear
    4. N - Parameter Polynomial Fitting
    5. Polynomial and Rational Function Approximation

Prerequisites: MATH 240, 320 and CPSC 111 or CPSC 211

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