Math 304 (Spring 2012)

Math 304, Numerical Methods (Spring 2012)
Lectures: Monday, Wednesday 15:30-16:45 at SOS B21

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

Office Hours:
Mon 11:00-12:00, Fri 10:00-11:00
or by appointment

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

Office Hours:
Thr 17:30-19:00 or by appointment

Course Description:

The course covers various topics in numerical analysis. The emphasis will be put on the numerical solutions of linear systems, non-linear systems, integrals and ordinary differential equations. We will also touch on topics such as the least squares problem and interpolation that are commonly used to analyze and approximate large-scale data. We will develop numerical algorithms for these main-stream problems, and analyze their accuracy and efficiency. Convergence of the iterative algorithms, for instance for nonlinear systems, will be discussed. In the homeworks you will apply the numerical algorithms to realistic applications.

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

Announcements:

The final will take place on May 24th, Thursday between 15:00-18:00 at ENG B30.

Topics: All topics covered throughout the semester are included. About half of the questions will concern the topics (the Gaussian quadrature and numerical differentiation) not covered in the midterm.
Office Hour: May 23rd, Wednesday (at SCI 114) between 13:00-15:30.

Homework 5 mostly concerns the Gaussian quadrature and numerical differentiation, and is due on May 30th, Wednesday.

Matlab files for homework 5 - Euler.m, midpoint.m, fun_ODE.m generate_fun.m, fun_real_trig.m.

Have a look at the second midterm and solutions.

Text:

The first text will be available at the photocopy room in the student center. The second will be made available at the reserve desk in the library. You could also buy the second book from the bookstore.

Lecture Notes from Spring 2010, by Emre Mengi
Numerical Analysis, 9th Ed. by Richard L. Burden and J. Douglas Faires

Supplementary Books:

Admittedly the first four books below are advanced. They are intended for ambitious students.The first three will be available at the reserve desk in the library. 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).

Numerical Linear Algebra by Lloyd N. Trefethen and David Bau
Fundamentals of Matrix Computations, 2nd Ed by David S. Watkins
A First Course in the Numerical Analysis of Differential Equations, 2nd Ed by Arieh Iserles
Numerical Mathematics by Alfio Quarteroni, Riccardo Sacco and Fausto Saleri
Numerical Computing with Matlab, Cleve Moler (freely 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.)

Resources:

Problem Session Notes (by Courtesy of Mustafa Kılıç)

Week 1 (Feb13-17)

An introductory Matlab manual
Brief notes on IEEE floating-point arithmetic by Michael L. Overton (Ignore the title IEEE floating point numbers ``in Java". Everything here, except the last two subsections on page 11, applies to Matlab.)

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

Homework 1 (due March 2)

Matlab files for hw1: bisection.m, fixedpoint.m, Newton.m

Homework 2 (due March 16)

Matlab file for hw2: forwardsubstitute.m

Homework 3 (due April 6) - Solutions

Matlab files for hw3: backsubstitute.m, forwardsubstitute.m

Homework 4 (due April 30)

Matlab file for hw4: Newton.m

Homework 5 (due May 30)

Matlab files for hw5: Euler.m, midpoint.m, fun_ODE.m generate_fun.m, fun_real_trig.m

Midterm:
The tentative midterm dates are March 14 for the first midterm, and April 25 for the second midterm. These dates will be made definite after taking your exam schedules in account.

Final:
The final date and location will be announced towards the end of the semester.

Exams and Solutions:

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

February 6, Monday --- First Day of Classes
February 8-10 --- Add-Drop Period
March 30, Friday --- Deadline to Withdraw
April 9-13 --- Spring Break
April 23, Monday --- National Sovereignty and Children's Day
May 1, Tuesday --- Labor and Solidarity Day
May 18 --- Last Day of Classes