CENG 375 Numerical Computations

Summer 2005

Most recent announcement: Aug10

Announcements

Watch this space for the latest updates. Last updated: 10.Ağustos.2005 11:55 You can see your grades from Student Information System, the distribution of the grades is given.

August 9, 2005 16:02 The evaluation of the final exam is completed. It is posted to the announcement board near my office. The solutions are given , see Course Schedule section.

The grades for the quiz7-9 is given, see Course Schedule section.

August 6, 2005 20:11 The assignments should be submitted before final exam both in paper and in electronic format. You are supposed to submit either via e-mail or with floppy diskette. The format is as all files compressed to one file with the name like studentid.zip. You will be asked about your assignments at afternoon. The time and list will be announced.

August 4, 2005 14:18 The lecture notes for the seventeenth lecture is available, see Course Schedule section.

August 3, 2005 16:55 The evaluation of the midterm exam is completed. It is posted to the announcement board near my office.

July 31, 2005 18:13 The past year's final examination questions is available.

July 31, 2005 18:00 The lecture notes for the sixteenth lecture is available, see Course Schedule section.

July 29, 2005 14:26 The lecture notes for the fifteenth lecture is available, see Course Schedule section. Final exam will be held on Monday Aug 8, 2005 at 09.00.

July 27, 2005 16:59 The lecture notes for the fourteenth lecture is available, see Course Schedule section.

July 25, 2005 15:03 The grades for the quiz3-6 is given, see Course Schedule section.

July 23, 2005 15:54 Third assignment is published, it is due to end of the semester.The hands-on sessions notes for the thirteenth lecture is available, see Course Schedule section.

July 22, 2005 13:56 The lecture notes for the twelfth lecture is available, see Course Schedule section.

July 20, 2005 16:25 The solutions for the midterm exam is given.

July 17, 2005 16:04 Second assignment is published, it is due to end of the semester.

July 15, 2005 14:34 The lecture notes for the nineth lecture is available, see Course Schedule section.

July 13, 2005 12:58 The grades for the quiz2&3 is given, see Course Schedule section.

July 13, 2005 11:27 The lecture notes for the eighth lecture is available, see Course Schedule section.

July 10, 2005 17:18 The hands-on sessions notes for the seventh lecture is available, see Course Schedule section.

July 8, 2005 13:37 The lecture notes for the sixth lecture is available, see Course Schedule section.

July 7, 2005 11:04 The grades for the quiz1 is given, see Course Schedule section.

July 6, 2005 17:07 The lecture notes for the fifth lecture is available, see Course Schedule section.

July 3, 2005 18:46 The hands-on sessions notes for the fourth lecture is available, see Course Schedule section. First assignment is published, it is due to end of the semester.

July 1, 2005 11:12 The lecture notes for the third lecture is available, see Course Schedule section.

June 29, 2005 17:07 The lecture notes for the second lecture is available, see Course Schedule section. All the m-files (for lecturing and hands-on sessions) will be accessible via the link.

June 26, 2005 13:12 In the first lecture, there will be first metting (A319)and also in the second hour (INT3), we will make an introduction to the MATLAB, 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 is one group for lecturing. You will be expected to do significant programming assignments, as well as run programs we supply and analyze the output in hands-on sessions. 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 lecture, you will have a quiz (15 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

  • 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; x=g(x) Method

    • Other Rearrangements

    • Order of Convergence

  • Multiple Roots

  • The fzero function

  • 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

  • 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

• 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

• 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

  • 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

• 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.