Scope: This course is an introduction to a broad range of numerical methods for solving mathematical problems that arise in Science and Engineering. The goal is to provide a basic understanding of these numerical methods. This will help you choose and apply the appropriate numerical techniques for your problem and interpret the results.

Topics covered: Solution of systems of linear equations, Gaussian elimination and LU decomposition, Floating Point Arithmetic, Linear Least Squares, Regularized Least Squares, Data Assimilation, Solution of Nonlinear Equations, Polynomial Interpolation, Integration, Solution of Ordinary Differential Equations, Applications and Modeling.


Prerequisites: Basic Linear Algebra. Some knowledge in MATLAB programming helps.

Textbook: "Numerical Computing with MATLAB" by Cleve Moler.
Available online free of charge at http://www.mathworks.com/moler/

Course workload: Homework will be assigned roughly once a week, mostly with MATLAB programming assignments and one final take-home project.

Credits: 3 credit hours

Instructor: Dmitriy Leykekhman
Office Hour: 10:00-10:11 a.m. Wednnesday and Firday
Course webpage: http://www.math.uconn.edu/~leykekhman/courses/MATH3795/math3795.html

Syllabus

15 weeks.

This is intended schedule and most likey will be chahged during the semester.

Week 1: Basic Matlab.
Week 2: Floating Point Arithmetic.
Week 3: Solution of systems of linear equations. Gaussian eliminatio and LU decomposition.
Week 4: Special cases. Symmetric and banded matrices. Sensitivity of the Solution of a Linear System.
Week 5: Linear Least Squares. Normal Equation. QR-Decomposition.
Week 6: SVD-Decomposition. Regularized Least Squares.
Week 7: Applications. Data Assimilation.
Week 8: Total Least Squares.
Week 9: Solution of Nonlinear Equations.
Week 10: Polynomial Interpolation. Numerical Integration.
Week 11: Solution of Ordinary Differential Equationss.
Week 12: Mathmeatical Modelling. Applications.
Week 13: Mathmeatical Modelling. Applications.
Week 14: Student project presentations.
Week 15: Student project presentations.