CENG 375 Numerical Computations
Fall 2007

Most recent announcement: Feb13

Announcements

Watch this space for the latest updates. Last updated:13.Şubat.2008 11:37 Distribution of the grades is given.

January 18, 2008 11:04 Your midterm and final grades entered to the sql database, check “ogrenci bilgi sistemi” of registary office to see your marks. Other marks are available as grades. Please see me for any typo errors as sso as possible or just send an e-mail.

January 15, 2008 14:52The list of the students that I have Doctor's written excuse;

• Dogus Tunga Atasoy - Midterm

• Yasar Deniz Gokyer - Midterm

• Zeynep Kaya - Final

• Sevil Arslan

• Hakan Altiaylik

January 15, 2008 14:30 There will be a make-up exam on Thursday at 13.00. If you have any valid excuse, send an e-mail to me and then sit in this make-up exam. if you don't have any doctor's written excuse at the moment, you should either see me or just take the exam, but the result will not be valid until i received a valid report.

January 14, 2008 15:30 URGENT. I will submit your grades at Jan 18, 2008 Friday. I will not available following week. Please see me in this week for any reason if you have any excuse (doctor's writen report etc.).

January 4, 2008 14:49 Several sample questions for the exam preperation is available. Also, the midterm exam questions are available (see Course Schedule section).

December 24, 2007 14:50 The lecture notes and hands-ons for twelfth week is published, see Course Schedule section. The fourth assignment is published and due to January 07, 2008. There will be some example questions regarding to the final exam. It will be published later.

December 12, 2007 13:13 There will be no lab hours today. Please attend Friday and Tuesday sessions. Also, there will be a recitation session (solving midterm questions) at next tuesday. Since there is a religional holiday at the next week, no thursday lecture section and lab hours including tuesday section after holiday.

December 4, 2007 09:30 The lecture notes and hands-ons for eleventh week is published, see Course Schedule section. The third assignment is published and due to December 14, 2007.

November 29, 2007 17:36 You should have calculator in the exam (preferably scientific calculator).

November 26, 2007 15:36 Quiz grades are available, see Course Schedule section. We have a password protection mechanism (username: cankaya password: cankaya).

November 15, 2007 11:31 There will be reviews in next week's lecture and lab hours. Those are missing the previous Tuesday lab hour (since i was not available) can attend at these hours to compensate the missing hour.

November 15, 2007 11:29 The lecture notes and hands-ons for eight is published, see Course Schedule section. The third assignment will be published soon.

November 6, 2007 14:09 The lecture notes and hands-ons for seventh week is published, see Course Schedule section

October 29, 2007 20:29 Second assignment is given, due to November 13, 2007.

October 29, 2007 20:24 The lecture notes and hands-ons for sixth week is published, see Course Schedule section

October 25, 2007 18:18 For assignments, you should submit the code via e-mail as

• Compressed all files to one file with tar or zip format

• Name this file as “yourstudentID.zip/tar/rar/tgz/gz” otherwise your code will not be evaluated.

you should also submit your code and your results (tables, plots, comments,...) in paper.

October 23, 2007 00:36 The lecture notes and hands-ons for fifth week is published, see Course Schedule section.

October 14, 2007 21:59 First assignment is given, due to October 30, 2007.

October 14, 2007 18:21 The lecture notes and hands-ons for fourth week is published, see Course Schedule section.

October 8, 2007 23:37 The monday lab session is closed due to the lack of students. Please attend to other sessions. If there is no suitable lab session other than monday, contact with me as soon as possible.

October 8, 2007 23:36 The lecture notes and hands-ons for third week is published, see Course Schedule section.

October 5, 2007 02:39 The lecture notes for second week is published, see Course Schedule section.

October 5, 2007 01:31 There will be no lecture at October 11, 2007 because of the Ramadan Holiday. Thursday' section studensts should attend to the Tuesday's class for next week. Those of the students who are not able attend to second wee'ks lecture and/or third week's lecture should send to me an E-mail or inform me by any means. So that we will have an additional lecture hour for covering these two weeks.

October 3, 2007 12:33 All the m-files (for lecturing and hands-on sessions) will be accessible via the link.

October 3, 2007 12:33 The Hands-on for second week is published, see Course Schedule section.

October 3, 2007 12:31 THIS WEB PAGE IS FINALLY AVAILABLE. In the first lecture, there will be first metting. The lecture notes for the second week will be published soon, see Course Schedule section.

Overview

Ceng 375 is intended to provide an understanding of the most useful numerical algorithms, an ability to organize problems in a form suitable for such numerical solutions, and an introduction to common computer methods for their implementation. This course is an introduction to numerical analysis. Topics include the analysis of error, the use of computers as numerical computing devices, programming in MATLAB, direct and iterative methods for linear equations, nonlinear equations, interpolation and function approximation, numerical differentiation and integration.

• Students will be able to recognize common types of numerical problems encountered in engineering practice as described in the class schedule.

• Students will be able to set up a numerical solution for these problems.

• Students will be able to select an appropriate method for the solution of these problems.

• Students will be able to use an appropriate method to solve these problems.

• Students will be able to check the reasonableness and validity of their solution.

Lecture Information

There are two groups for lecturing, you may attend any one of the lecture hours but not for the Friday's lecture. Please attend your predefined sessions regularly on Friday. You will be expected to do significant programming assignments, as well as run programs we supply and analyze the output. These programs will be written in MATLAB (it will be easiest to learn), a widely used languge for numerical computing (learning MATLAB is part of the course). For programming assignments, other languages will be accepted; but no programming assistance will be given for such languages (e.g. Fortran, C/C++, and Java).

We require single variable calculus and a knowledge of computer programming. A knowledge of linear algebra and differential equations is also helpful. You should review Taylor's theorem, differential equations, and linear algebra, in particular systems of linear equations. Those of you who do not know how to program will be expected to learn very quickly.

You will have quizes (15 minutes, may be less; but not scheduled as before) for the previos lecture's subjects. There won't be any make-up for these quizes and they will have weight for the final grading.

Important announcements will be posted to the Announcements section of this web page above, so please check this page frequently. You are responsible for all such announcements, as well as announcements made in lecture.

Course Outline

• Contents

• List of Tables

• List of Figures

• Introduction to MATLAB

• Preliminaries

  • Analysis vs Numerical Analysis

  • Computers and Numerical Analysis

  • An Illustrative Example

  • Some disasters attributable to bad numerical computing

  • Kinds of Errors in Numerical Procedures

  • Parallel and Distributed Computing

    • Speed -up and Efficiency

  • Measuring the Efficiency of Numerical Procedures

    • Taylor Series

    • Polynomials

  • Hands-on - Preliminaries

• Solving Nonlinear Equations

  • Interval Halving (Bisection)

  • Linear Interpolation Methods

    • The Secant Method

    • Linear Interpolation (False Position)

  • Newton's Method

  • Hands-on-Solving Nonlinear Equations with MATLAB I

  • Muller's Method

  • Fixed-point Iteration; Method

    • Other Rearrangements

    • Order of Convergence

  • Multiple Roots

  • The fzero function

  • Nonlinear Systems

    • Solving a System by Iteration

  • Hands-on- Solving Nonlinear Equations with MATLAB II

  • Assignment 1 - Solving Nonlinear Equations

• Solving Sets of Equations

  • Matrices and Vectors

    • Some Special Matrices and Their Properties

    • Using Computer Algebra Systems

  • Elimination Methods

    • Gaussian Elimination

    • The Gauss-Jordan Method

    • Using the LU Matrix for Multiple Right-Hand Sides

  • Hands-on-Solving Sets of Equations with MATLAB I

  • The Inverse of a Matrix and Matrix Pathology

    • Pathological Systems

    • Redundant Systems

  • Ill-Conditioned Systems

    • Norms

      • Matrix Norms

  • Iterative Methods

    • Jacobi Method

    • Gauss-Seidel Iteration

    • Sparse Matrices and Banded Matrices

  • Parallel Processing

  • Hands-on- Solving Sets of Equations with MATLAB II

  • Assignment 2 - Solving Sets of Equations

• Interpolation and Curve Fitting

  • Interpolating Polynomials

    • Interpolation versus Curve Fitting

    • Fitting a Polynomial to Data

    • Lagrangian Polynomials

    • Neville's Method

  • Divided Differences

  • Interpolation and Curve Fitting with MATLAB I

  • Spline Curves

    • The Equation for a Cubic Spline

  • Least-Squares Approximations

    • Nonlinear Data (Curve Fitting)

    • Least-Squares Polynomials

    • Use of Orthogonal Polynomials

  • Interpolation and Curve Fitting with MATLAB II

  • Assignment 3 - Interpolation and Curve Fitting; Due to December 14, 2007

• Approximation of Functions

  • Chebyshev Polynomials and Chebyshev Series

    • Chebyshev Polynomials

    • Economizing a Power Series

    • Chebyshev Series

  • Chebyshev Polynomials; Approximation of Functions with MATLAB I

  • Fourier Series

    • Fourier Series for Periods Other Than

    • Fourier Series for Nonperiodic Functions and Half-Range Expansions

    • Summary

  • Hands-on-Fourier Series; Approximation of Functions with MATLAB II

  • Assignment 4 Fourier Series; Approximation of Functions; Due to January 07, 2008

• Numerical Differentiation and Integration

  • Differentiation with a Computer

    • Extrapolation Techniques

  • Numerical Integration - The Trapezoidal Rule

    • The Trapezoidal Rule

    • The Composite Trapezoidal Rule

  • Hands-on-Numerical Differentiation and Integration with MATLAB

• vita

• About this document ...

Text Book

Required

Readings will be assigned in Numerical Analysis 7th Edition (International Edition) Curtis Gerald, Patrick Wheatley, ISBN: 032119019X Sep 2003.

Recommended

• Numerical Computing with Matlab Cleve B. Moler, ISBN: 0898715601 January 1, 2004.

• Numerical Methods Using Matlab 4th Edition (International Edition) John Mathews, Kurtis Fink, ISBN: 0131911783 Jan 2004.

• "Numerical Recipes in Fortran" or "Numerical Recipes in C", Second Edition, W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Cambridge University Press, 1992.

This texts are only recommended rather than required. This books are useful for reference, for an alternative point of view.

Online References

Some materials are given. Please inform me about the usefullness of the materials. Check this place for updates.

The following references are available online

• MATLAB home site.

• A Matlab tutorial from the University of New Hampshire

• Matlab tutorial - US Naval Academy

• Matlab tutorial - University of British Columbia

• Matlab tutorial - University of Florida

• Matlab Tutorial - University of California at Los Angeles

• Mathtools.net: a technical computing portal for scientific and engineering needs.

Grading Criteria

• There will be a midterm and a final exam, will count 20% and 40% of your grade, respectively.

• Quiz: 15% (worst of the quizes will be discarded)

• Assignments (or Term Project): 15%

• Attendance is required and constitutes part of your course grade; 10%

Policies

• Attendance is not compulsory, but you are responsible for everything said in class.

• I encourage you to ask questions in class. You are supposed to ask questions. Don't guess, ask a question!

• You may discuss homework problems with classmates (although it is not to your advantage to do so).

• You can use ideas from the literature (with proper citation).

• You can use anything from the textbook/notes.

• The code you submit must be written completely by you.

Course Schedule

The following schedule is tentative; it may be updated later in the semester, so check back here frequently.