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. |
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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. |
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PREREQUISITES: | CS 144 and either Math 341 or Math 316. Math 301 preferred. | ||
OTHER: | |||
EFFECTIVE DATE: | August 2001 |