MCS 331 Numerical Methods
Fall 2013

Most recent announcement: Jan07

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:

January 7, 2014 Final exam date and place: 19/01/2014 12:30 N-B06 (Central Campus)

December 22, 2013 The evaluation of midterm exam papers is completed, check your sql server.

November 5, 2013 Course Schedule is revised.

October 11, 2013 Grading Criteria is revised.

September 30, 2013 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. All the example m-files (for lecturing and hands-on sessions) will be accessible via link.

Lecture Information

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.

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

Mcs 331 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

• 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

  • Assignment 1 - Solving Nonlinear Equations; Due to December 5, 2011

  • 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 25, 2011

• 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

• 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

  • Assignment 3 - Interpolation and Curve Fitting; Due to January 07, 2012

• 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 25% and 45% of your grade, respectively.

• Laboratory Examination 20%

• Assignments (or Term Project): 10%

• Attendance is required and constitutes part of your course grade as bonus; 5%

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.