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 Email: emengi@ku.edu.tr Phone: 338-1658
Teaching Assistant:
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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 (See the course syllabus for issues such as grading and the formats of the exams.) Announcements:
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Textbooks:
The textbook can be bought from the bookstore. It will also be available at the reserve desk in the library.
- Applied Numerical Analysis Using Matlab 2nd Edition, Laurene V. Fausett
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.
- Fundamentals of Matrix Computations 2nd Edition, David S. Watkins
- Numerical Mathematics, Alfio Quarteroni, Riccardo Sacco and Fausto Saleri
Resources:
- Matlab Routines
- Inner product of two vectors: innerproduct.m
- Matrix vector product: matvectime.m
- Forward substitution: forwardsubstitute.m
- Gaussian elimination: gaussian_elimination.m
- Gaussian elimination with partial pivoting: gaussian_elimination_pivoting.m
- Construct the orthogonal factor of QR factorization using Householder vectors: constructq.m
- Rayleigh iteration: rayleigh_iter.m
- Newton’s method for nonlinear systems: Newton.m
- Slides for some of the lectures
- 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.)
- Matlab Clones (These are free softwares -almost- compatible with Matlab. If you have a personal computer, you can install one of these and do the computational hws in these platforms instead of Matlab.)
Homeworks: All hws are due by 16:00 on the indicated dates below.
Midterm: |
Final: The final will be held on June 11th from 15:00 till 18:00 at ENG Z16. Important Enrollment Dates and Holidays:
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