Office: SCI 267
Uğur Mümtaz Birbilen
Office: ENG 209
This course covers some of the most fundamental topics in numerical analysis. The first part concerns numerical linear algebra. We will introduce numerical algorithms for the solutions of linear systems, linear least squares problems (best approximate solution for an inconsistent linear system) and eigenvalue problems. In each case we will analyze the efficiency and accuracy of the algorithm in the presence of rounding errors. Special emphasis will be put on matrix factorizations, in particular LU and QR factorizations.
In the second part we will learn how to solve nonlinear systems mainly by using Newton's method. As a special application we will consider unconstrained optimization. Then we will spend some time on interpolation and numerical integration. Finally we will focus on the numerical solution of differential equations.
There will be a fine balance between theoretical and computational issues. Convergence of
the iterative algorithms, for instance for eigenvalue problems and nonlinear systems, will be analyzed. At the very least we will justify why these algorithms converge to the actual solution and how quickly they converge. In the homeworks you will apply these numerical algorithms to real world problems.
(See the course syllabus for issues such as grading and the formats of the exams.)
All hws are due by 16:00 on the indicated dates below.
The midterms will be held during the regular lecture hour on the following dates.
The final will be held on June 11th from 15:00 till 18:00 at ENG Z16.
Important Enrollment Dates and Holidays:
(Holidays are underlined.)