Math 304, Numerical Methods (Spring 2010)
Lectures: Mon and Wed between 15:30-16:45 at SOS Z27
Problem Sessions: Fri between 9:30-10:45 at SOS Z12




Instructor:
Emre Mengi
Office: SCI 267
E-mail: emengi@ku.edu.tr
Phone: 338-1658
Office Hour:
Thr 9:00-11:00
or by appointment



Teaching Assistant:
Uğur Mümtaz Birbilen
Office: ENG 209
E-mail: ubirbilen@ku.edu.tr
Office Hour:
Tue 15:00-16:00






Course Description:
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.)


Announcements:
  • FINAL
    • will be held on June 11th, Friday at ENG Z16 from 15:00 till 18:00.
    • All topics are included with emphasis on numerical differentiation.
    • Make sure to go over all of the homeworks. 
    • Also solve the practice final. This may be a bit longer than the actual final. However, it is a good indicator of whether you are ready to the final or not.
    • There will be a review lecture on June 7th, Monday at SCI Z33 from 16:00 till 18:00.   
    • Have a look at the solutions to homework 8.
  • The ninth homework concerns systems of ordinary differential equations, higher order differential equations and the solution of Poisson equation using finite difference formulas.

Textbooks:
The textbook can be bought from the bookstore. It will also be available at the reserve desk in the library.

Supplementary Books:
An electronic copy of the book by Quarteroni, Sacco and Saleri can be accessed through library (visit the website http://libunix.ku.edu.tr/ and search for this book). The book by Watson is available at the reserve desk in the library.
Resources:

Homeworks:
All hws are due by 16:00 on the indicated dates below. 

Midterm:
The midterms will be held during the regular lecture hour on the following dates.
Final:
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.)
  • February 15th, First Day of Classes
  • February 17th-19th, Add-drops
  • March 12th, Last Day to Withdraw
  • April 5th-9th, Spring Break
  • April 23rd (Fri), National Sovereignty and Children's Day
  • May 19th (Wed), Youth and Sports Day
  • May 28th, Last Day of Classes
  • June 1st-11th, Finals