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Numerical Analysis
NUMERICAL ANAL
CLASS CODE: MATH 411 CREDITS:  3
DIVISION: PHYSICAL SCIENCE & ENGINEERING
DEPARTMENT: MATHEMATICS
GENERAL EDUCATION: This course does not fulfill a General Education requirement.
DESCRIPTION: Basic error analysis, complexity of algorithms, roots, interpolation, least squares approximation, curve fitting, numerical differentiation and integration, and systems of linear equations.
TAUGHT: Winter even years
CONTENT AND TOPICS: Basic error analysis, complexity of algorithms, roots, interpolation, least squares, approximation, curve fitting, numerical differentiation and integration and systems of linear equations.
GOALS AND OBJECTIVES: 1. Describe the difficulties that can arise when solving problems using numerical procedures. List possible sources of error.
2. Give conditions under which a method of iterations will converge to a solution and show it converges in a particular case. Describe the type of convergence.
3. Apply the methods of bisection, secant and Newton to solve a non-linear equation.
4. Apply the Newton-Raphson method to solve a system of non-linear equations.
5. Describe and use the methods of Jacobi, Gauss-Seidel and SOR to solve a system of linear equations. Give conditions for convergence for each method.
6. Use the power method to find the largest eigenvalue of a given matrix.
7. Find the LU factorization of a matrix. Use the factorization to solve a system of linear equations.
8. Understand and apply numerical differentiation techniques.
9. Apply various interpolation and approximation techniques.
REQUIREMENTS: All students must have their own textual materials.
If a graphing calculator is required, the student must supply it.
Exams are required by all faculty members as is homework and a limited amount of computer programming. Each faculty member decides what other forms of assessment to require and what weight to give them.
PREREQUISITES: CS 144 and either Math 341 or Math 316. Math 301 preferred.
OTHER:
EFFECTIVE DATE: August 2001