Math 504 (Fall 2011)

Math 504, Numerical Methods I (Fall 2011)
Lectures: Monday, Wednesday 12:30-13:45 at ENG B05

Instructor:
Emre Mengi
Office: SCI 114
E-mail: emengi@ku.edu.tr
Phone: (212)338-1658

Office Hours:
Thr 15:30-17:00 or by appointment

Teaching Assistant:
Mustafa Kilic
Office: SCI 111
E-mail: mukilic@ku.edu.tr

Office Hours:
Tue 13:00-14:00
Wed 11:00-12:00 or by appointment

Course Description:

This course concerns the numerical solution of linear systems, linear least squares problems (best approximate solution for an inconsistent linear system), eigenvalue and singular value problems. We will introduce numerical algorithms for the solution of these problems on a computer, and analyze their efficieny and accuracy in the presence of rounding errors. For the numerical solutions of the problems matrix factorizations will be introduced, and their existence and uniqueness will be discussed. The Krylov-subspace based iterative algorithms will be studied as much as time permits.

(See the course syllabus for issues such as grading, a crude course calendar and the formats of the exams.)

Announcements:

The final will be held on January 4th, Wednesday at 12:00 at ENG Z15. The format will be the same as the midterms. In particular it will be an open-notes, but a closed book exam. All topics are included in the final, but the emphasis will be on the topics covered after the second midterm (eigenvalue problems, Krylov subspace methods).

Office Hours before the Final

Thr, Dec 29th 13:45-15:15 (E. Mengi, SCI 114)
Mon, Jan 2nd 15:15-17:15 (E. Mengi, SCI 114)
Tue, Jan 3rd after 11:00; Mustafa Kilic will be usually in his office SCI 111.

Homework 5 is due on January 10th, Tuesday by 11:00. This homework concerns the eigenvalue problems, their numerical solution and Krylov subspace methods. The deadline is tight.

Solutions to homework 4 (By courtesy of Mustafa Kilic)

Textbooks:
Both of the textbooks will be available at the reserve desk in the library.

Numerical Linear Algebra, Lloyd N. Trefethen and David Bau
Fundamentals of Matrix Computations (2nd Edition), David S. Watkins

Supplementary Books:

Numerical Computing with Matlab, Cleve Moler (Available at http://www.mathworks.com/moler/index_ncm.html)
Numerical Computing with IEEE floating point arithmetic, Michael L. Overton (see the brief notes below under the resources extracted from this book. If you think you will be frequently involved in IEEE arithmetic, this book is relatively cheap when bought from the SIAM website.)
Matrix Computations 3rd Edition, Gene H. Golub and Charles F. Van Loan (available at the reserve desk in the library)

Resources:

Lecture Notes

New, Fall 2011

Old, Fall 2010

Homeworks:
All hws are due by 5pm on the indicated dates below unless otherwise indicated.

Homework 1 (due October 21, Friday) - Solutions

Supplementary Files : taurus.jpg, orthogonalize.m, lrsvecs.m

Homework 2 (due November 4, Friday) - Solutions
Homework 3 (due November 25, Friday) - Solutions

Supplementary Files : constructq.m

Homework 4 (due November 16, Friday) - Solutions

Supplementary m-files : forwardsubstitute.m, backsubstitute.m, growth_factor.m,plot_growth_factor.m, plot_condition_number.m, random_growth_factor.m, accuracy.m, accuracy2.m, accuracy3.m

Homework 5 (due on January 10, Tuesday)

Midterm:
The first midterm took place on October 27, Thursday. The second took place on December 8th, Thursday.

Final:
The final will be held on January 4th, Wednesday at 12:00 at ENG Z15.

Exams and Solutions:

Important Enrollment Dates and Holidays:
(Holidays are underlined.)

September 19, First day of classes
September 21-23, Add-drops
October 28th-29th, Foundation of Republic of Turkey
November 7-11, Kurban Bayramı
December 30, Last day of classes
January 4-14, Finals