MATHS 363: Numerical Analysis 2 (3)

Syllabus

  1. Prerequisites: MATHS 217 and either MATHS 362/562 or CS 362/562; or permission of department chairperson.

 

2.       Course Description: Topics include direct and iterative methods for solving systems of linear equations, eigenvalue problems; minimization of functions and linear programming. Includes programming of numerical algorithms.

 

3.       Course Objectives: The objective of numerical analysis is to find algorithms that solve models efficiently and accurately. This is typically achieved by implementing the algorithms on a computer and analyzing the results. This course will complete the students' introduction into the basic theory and practice of numerical methods.

 

4.       Course Rationale: Not all problems lend themselves to closed form solutions. Therefore, this course will serve the student interested in studying numerical and/or computer techniques applied to  problems arising in Linear Algebra and other mathematical disciplines.

 

5.       Course Content: Specific topics will include Gaussian elimination, tri-diagonal and banded matrices, LU and Cholesky factorization, iterative methods for solving systems of linear equations, eigenvalues and eigenvectors, Singular Value Decomposition, Power method,  minimization of functions, linear programming.

 

  1. Course Format: A comprehensive semester course will cover the topics mentioned above. The class lectures will develop, investigate, and apply the main ideas of the course. Computer projects are used to help understand the fundamental principles.

 

  1. Methods of Evaluating Student Performance: Course grades are determined primarily by student performance on tests and computer assignments and projects, as well as possibly quizzes, homework, and class participation. Students are evaluated on content material and on their ability to communicate this material to others orally and/or in writing. The evaluation and weight of these various components are at the discretion of the individual instructor.

 

  1. Evaluation of the Course: The instruction of the course is evaluated by departmental student evaluations and peer evaluations. The course is reviewed and revised periodically by the Departmental Undergraduate Programs Committee.

 

I. Livshits, 3/2007