CENG 375 Numerical Computations
Fall 2004

Most recent announcement: Jan31

Announcements

Watch this space for the latest updates. Last updated: 31.Ocak.2005 15:08 Distribution of the grades is given.

January 28, 2005 14:02 Evaluation of the final exam is completed.

January 26, 2005 19:32 Your grades are entered as I, will be corrected until friday hopefully.

January 13, 2005 16:49 Make-Up exam for midterm and final exams will be on Jan 18, 2005 at 14.30. The list of the students that I have Doctor's written excuse;

Midterm:

Kerim Akman

January 9, 2005 16:57 Some suggested questions for the final exam preparation;

January 6, 2005 15:54 The grades for the quizes are available, see Course Schedule section.

December 28, 2004 10:01 The date and exam places for Final exam is announced, see Course Schedule section.

December 21, 2004 12:37 The lecture notes for the thirteenth week is published, see Course Schedule section.

December 14, 2004 11:41 The lecture notes for the twelfth week is published, see Course Schedule section.

December 13, 2004 16:09 The date for Final exam is announced, see Course Schedule section.

December 13, 2004 16:09 The evaluation of the midterm exam papers is completed, see Course Schedule section.

December 10, 2004 10:44 Third assignment is published. It is due to December 24, 2004.

December 6, 2004 19:22 The grades for the third quiz are available, also the lecture notes for the tenth week is published, see Course Schedule section.

November 30, 2004 11:06 The lecture notes for the tenth week is published, see Course Schedule section.

November 23, 2004 11:34 The lecture notes for the nineth week is published, see Course Schedule section.

November 22, 2004 16:11The solutions for the midterm exam is available, see Course Schedule section.

November 12, 2004 18:21There will be lecture and lab sessions as usual at the week after the Ramadan Holiday.

November 10, 2004 18:35 The grades for the third quiz are available, see Course Schedule section. The solutions for the hands-on sessions are also available.

November 8, 2004 15:28 You may use calculator in the midterm exam.

November 8, 2004 15:19 For assignments,

you should submit the code via e-mail or flooppy disk as

• Compress all files to one file with tar or zip format.

• Name this file as yourstudentID.zip

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

Only sending the code will not be accepted.

November 5, 2004 10:59 Second assignment is published. It is due to Nov 26, 2004.

November 1, 2004 15:18 The lecture notes for the sixth week is published, see Course Schedule section.

October 26, 2004 17:45 The lecture notes for the fifth week is published, see Course Schedule section.

October 25, 2004 17:14 THERE WILL BE NO LECTURES IN THAT WEEK Since 28-29 October 2004 Republican Day (One and a Half Day). Lecture will be done on Nov 1, 2004 Monday at 16.40-18.40.

October 22, 2004 10:52 First assignment is published. It is due to Nov 5, 2004.

October 21, 2004 10:55 The date for Midterm exam is announced, see Course Schedule section.

October 20, 2004 16:12 The grades for the quizes are available, see Course Schedule section.

October 18, 2004 12:52 The lecture notes for the fourth week is published, see Course Schedule section. The typing errors in the second week's lecture notes are corrected. The solutions for the third week's hands-on are available.

October 15, 2004 10:38 The lab notes for the third week is published, see Course Schedule section.

October 12, 2004 11:04 The solutions for the second week's quiz is available, see Course Schedule section.

October 11, 2004 16:02 The lecture notes for the third week is published, see Course Schedule section.

October 9, 2004 20:37 The solutions for the second week's MATLAB study is available, see Course Schedule section.

October 7, 2004 18:44 The lab notes for the second week is published, see Course Schedule section.

October 1, 2004 10:03 The lecture notes for the practice session is published, see Course Schedule section.

September 30, 2004 14:13 The lecture notes for the second week is published, see Course Schedule section.

September 27, 2004 09:46 The Friday lecture' s place is changed as INT2. The lecture notes for the second week will be published soon.

September 23, 2004 16:18 In the first lecture, there will be first metting. The lecture notes for the second week is published, 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.

In the beginning of the each Friday's lecture, you will have a quiz (20 minutes, may be less) 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

  • Kinds of Errors in Numerical Procedures

  • Parallel and Distributed Computing

    • Speed -up and Efficiency

  • Measuring the Efficiency of Numerical Procedures

    • Taylor Series

    • Polynomials

  • Preliminaries with MATLAB

• Solving Nonlinear Equations

  • Interval Halving (Bisection)

  • Linear Interpolation Methods

    • The Secant Method

    • Linear Interpolation (False Position)

  • Newton's Method

    • Complex Roots

  • Solving Nonlinear Equations with MATLAB I

  • Muller's Method

  • Fixed-point Iteration; Method

    • Other Rearrangements

    • Order of Convergence

  • Multiple Roots

  • Nonlinear Systems

    • Solving a System by Iteration

  • Solving Nonlinear Equations with MATLAB II

• 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

  • 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

  • Solving Sets of Equations with MATLAB

• Interpolation and Curve Fitting

  • Interpolating Polynomials

    • 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

    • Least-Squares Polynomials

    • Use of Orthogonal Polynomials

  • Interpolation and Curve Fitting with MATLAB II

• Approximation of Functions

  • Chebyshev Polynomials and Chebyshev Series

    • Chebyshev Polynomials

    • Economizing a Power Series

    • Chebyshev Series

  • Approximation of Functions with MATLAB I

  • Fourier Series

    • Fourier Series for Periods Other Than

    • Fourier Series for Nonperiodic Functions and Half-Range Expansions

    • Summary

  • 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

  • Numerical Differentiation and Integration with MATLAB I

• 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.