CENG 375 Numerical Computations
Fall 2010

Most recent announcement: Jan25

Announcements

Watch this space for the latest updates (If the characters do not show properly, please try viewing this page with Unicode (UTF-8) encoding). Last updated:

25. January 2011 16:49 Distribution of the grades is given.

24. January 2011 11:22 There will be a make-up exam on Jan 25, 2011 Tuesday at 14:00 (the exam time is subject to change due to conflicts with other exams). The list of the students that I have Doctor's written excuse;

• Ramazan Özcan – Midterm

• Gökçe Kuvandik – Midterm

• Onur Erdem Çakır – Final

If your name does not appear in the list at the moment although you have doctor's written excuse, you should either see me and/or just take the exam. But the result will not be valid until i received a valid report.

17. January 2011 21:59 You should bring your calculators to the exam hall (preferably a scientific one).

13. January 2011 17:09 Quiz4 and Assignment3 grades are available, see Course Schedule section

7. January 2011 17:30 Quiz3 and Assignment2 grades are available, see Course Schedule section

5. January 2011 21:36 The lecture notes and lab. studies for fifteenth week is published, see Course Schedule section

5. January 2011 15:46 The evaluation of midterm exam papers is completed. Your midterm exam grades are available, check your sql server.

30. December 2010 23:50 Quiz2 grades are available, see Course Schedule section

30. December 2010 00:05 The lecture notes and lab. studies for fourteenth week is published, see Course Schedule section

December 19, 2010 11:23 The third assignment is given, see Course Schedule section. It is due to Jan 03, 2011. Read the following lines very carefully;

1. Compress all files to one file. Name this file as “yourstudentID.zip(/tar/rar/tgz/gz)” otherwise your assignment will not be evaluated.

2. When this file decompressed, all files should reside in a directory named with “yourstudentID”. otherwise your assignment will not be evaluated.

3. You should submit your code and results (tables, plots, comments,...) via e-mail to me and to TA. otherwise your assignment will not be evaluated.

4. You should also submit your code and results (tables, plots, comments,...) in paper to TA. otherwise your assignment will not be evaluated.

Submission deadline for the assignment is at 24.00 o'clock. There will be no extension. You should send your E-mails until this time. But, you may submit your reports on paper next day.

December 19, 2010 12:45 The lecture notes and lab. studies for thirteenth week is published, see Course Schedule section.

December 13, 2010 11:44 The lecture notes and lab. studies for twelfth week is published, see Course Schedule section.

December 6, 2010 01:01 The lecture notes and lab. studies for eleventh week is published, see Course Schedule section.

November 28, 2010 19:18:08 The second assignment is given, see Course Schedule section. It is due to Dec 13, 2010.

November 28, 2010 19:15 The lecture notes and lab. studies for tenth week is published, see Course Schedule section.

November 23, 2010 22:17 Quiz1 & Assignment1 grades are available, see Course Schedule section.We have a password protection mechanism (username: cankaya password: cankaya).

November 17, 2010 18:21 The lecture notes and lab. studies for nineth week is published, see Course Schedule section.

November 3, 2010 17:35 The lecture notes and lab. studies for sixth week is published, see Course Schedule section.

October 28, 2010 01:08 The first assignment is given, see Course Schedule section. It is due to Nov 07, 2010.

October 13, 2010 17:23 The lecture notes and lab. studies for third and fourth weeks are published, see Course Schedule section.

October 9, 2010 17:03 The link problems in pdf-files are corrected.

October 6, 2010 17:42 The lecture notes and lab. studies for second week is published, see Course Schedule section.

September 29, 2010 16:40 All the example m-files (for lecturing and hands-on sessions) will be accessible via link.

September 29, 2010 13:45 In the first lecture, there will be first meeting and tutorial for Matlab. The lecture notes for the second week will be published soon, see Course Schedule section.

Lecture Information

There are two groups for lecturing, you may attend any one of the lecture hours. 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 analyse 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, linear algebra, and 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 quizzes (10-15 minutes, may be less; but not scheduled as before) for the previous lecture's subjects. There won't be any make-up for these quizzes 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.

Overview

Ceng 375 is intended to provide an understanding of the numerical algorithms, an ability to organise 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 recognise 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.

Course Outline

• Contents

• List of Tables

• List of Figures

• First Meeting

  • Lecture Information

  • Overview

  • Text Book

  • Grading Criteria & Policies

  • Numerical Analysis/Computations

  • Introduction to MATLAB

    • Help

    • Assignment Statements

    • Relational Operators

    • Loops & Conditionals

    • Functions

    • Matrices & Arrays

    • Graphics

    • Numeric vs Symbolic Computation

• 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

  • Lab. Study: 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

  • Newton's Method, Continued

  • 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; Due to November 7, 2010

• 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

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

  • Using the LU Matrix for Multiple Right-Hand Sides

  • 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

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

  • Assignment 2 - Solving Sets of Linear Equations - Due to December 13, 2010

• Interpolation and Curve Fitting

  • Interpolating Polynomials

    • Interpolation versus Curve Fitting

    • Fitting a Polynomial to Data

    • Lagrangian Polynomials

    • Neville's Method

  • Hands-on-Interpolation and Curve Fitting with MATLAB I

  • Divided Differences

  • Spline Curves

    • The Equation for a Cubic Spline

  • Least-Squares Approximations

  • Hands-on-Interpolation and Curve Fitting with MATLAB II

    • Nonlinear Data, Curve Fitting

    • Least-Squares Polynomials

      • Use of Orthogonal Polynomials

  • Hands-on-Interpolation and Curve Fitting with MATLAB III

  • Assignment 3 - Interpolation and Curve Fitting; Due to January 03, 2011

• Approximation of Functions

  • Chebyshev Polynomials and Chebyshev Series

    • Chebyshev Polynomials

    • Economizing a Power Series

    • Chebyshev Series

  • Hands-on-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

• Numerical Differentiation and Integration with a Computer

  • Differentiation with a Computer

  • 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 quizzes 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.