CENG 375 Numerical Computations
Fall 2006

Most recent announcement: Jan 26

Announcements

Watch this space for the latest updates. Last updated: 26.Ocak.2007 15:23 Distribution of the grades is given.

January 22, 2007 16:20 Make-Up exam for midterm and final exams will be on Jan 23, 2007 at 13.00. The list of the students that I have Doctor's written excuse;

• Ercan Varol -- Midterm

• Hatice Seda Turkmen -- Midterm, Final

• Abdulhadi Dervisoglu -- Midterm

• Zeki Burak Ata -- Midterm

• Cagatay Basoglu -- Midterm

• Sevil Arslan -- Midterm

• Fatos Evin Bayramoglu -- Midterm

• Cagatay Bal -- Midterm

• Ismail Demiralp -- Midterm

For all the others; they should be sure that their medical reports be approved by Medical Center and I have received a copy of it. Otherwise, they will be allowed to sit in the make-up exam but their exam will not be graded.

December 28, 2006 17:23 The results for the fourth quiz of the Tuesday session is annnounced, see Course Schedule section. The solutions for the exams will be erased soon, be quick to download.

December 19, 2006 11:07 Fourth assignment is given it is due to Dec 29, 2006. For assignments, you should obey the rules that previously declared.

December 18, 2006 17:23 The lecture notes and Hands-on for the thirteenth week is published soon, see Course Schedule section.

December 11, 2006 18:34 The lecture notes and Hands-on for the twelfth week is published soon, see Course Schedule section. Third assignment is given it is due to Dec 26, 2006. For assignments, you should obey the rules that previously declared.

December 5, 2006 12:15 The lecture notes and Hands-on for the eleventh week is published soon, see Course Schedule section.

November 28, 2006 12:18 The lecture notes and Hands-on for the tenth week is published soon, see Course Schedule section.

November 17, 2006 17:21 Second assignment is given it is due to Nov 28, 2006. For assignments, you should obey the rules that previously declared.

November 17, 2006 17:14 The lecture notes and Hands-on for the nineth week is published soon, see Course Schedule section.

November 7, 2006 12:17 The lecture notes and Hands-on for the seventh week is published soon, see Course Schedule section.

November 3, 2006 18:48 Office Hours are rearranged, see the time table above.

October 30, 2006 18:59 The lecture notes and Hands-on for the sixth week is published soon, see Course Schedule section.

October 26, 2006 17:19 The possible exam date is Nov 17, 2006 at 12.40.

October 26, 2006 17:15 First assignment is given it is due to Nov 10, 2006. For assignments, you should submit the code via e-mail as

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

• Named this file as yourstudentID.zip otherwise your code will not be evaluated.

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

October 24, 2006 20:42 On Thursday lecture, there will be review and answering your questions. On Thursday Lab, there will be regular lab session. On Friday lab hours, there will be review and answering your questions.

October 16, 2006 19:21 The lecture notes and Hands-on for the fourth week is published soon, see Course Schedule section.

October 13, 2006 10:34 The Hands-on for third week is published, see Course Schedule section.

October 11, 2006 13:23 Tuesday lecture is held on A319 at 12.40.

October 10, 2006 12:17 The lecture notes for the third week is published soon, see Course Schedule section.

October 6, 2006 09:43 The Hands-on for second week is published, see Course Schedule section.

October 3, 2006 09:53 All the m-files (for lecturing and hands-on sessions) will be accessible via the link. The lecture notes for the second week is published, see Course Schedule section.

September 29, 2006 14:23 The lecture hour for the Tuesday session is again rearranged as 14.30-16.30 at the lecture hall A319 because of the rearrangement of the another “must” course. You should be present on Tuesday 12.30 at the lecture hall A319 to see possible problems. Anyway, the lecture will be held on either 12.40 or 14.40. Two new sessions for the hands-on are opened, see the schedule above.

September 28, 2006 12:52 The lecture hour for the Tuesday session is rearranged as 12.30-14.30 at the lecture hall A319. You should attend your predefined sections (for the Tuesday session) unless you have a valid excuse.

September 26, 2006 11:05 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

  • Midterm Related and Interpolation and Curve Fitting with MATLAB II

  • 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 III

• Approximation of Functions

  • Chebyshev Polynomials and Chebyshev Series

    • Chebyshev Polynomials

    • Economizing a Power Series

    • Chebyshev Series

  • Chebyshev Polynomials; Approximation of Functions with MATLAB I

  • Assignment 3 - Interpolation and Curve Fitting

  • 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

• 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 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.