Syllabus(Mat612) Obe

INSTITUT TECHNOLOGY MARACOURSE INFORMATION

Confidential

Code : MAT612

Course : Partial Differential Equation

Level : Bachelor of Science (Honours) Mathematics

Credit Unit : 3

Contact Hour : 4

Part : 5

Course Status : Core

Prerequisite : Intro to Numerical Analysis, Calculus III, Differential Equations, Linear Algebra

Course Objective : Upon completion of this course, students should be able to:

gain insight into the modeling process of a variety of systems represented by PDEs.

use mathematical software competently as a problem solving and visualizing tool in tackling PDE problems.

develop an intuitive understanding of the physical processes through mathematical investigations.

Course Description : This is an introductory partial differential equation (PDE) course, which emphasizes on the computational and modeling aspects of science and engineering.

Department of MathematicsFaculty Of Technology and Quantitative Sciences Bachelor of Science (Hons) (Mathematics)@ Hak Cipta Universiti Teknologi Mara

Year 2007

Learning outcomes On successful completion of the course, the students should be able to:

Classify a given PDE into its various categories.

Express and interpret simple heat and wave problems into parabolic, hyperbolic or elliptic BVPs vice versa

Solve classical BVPs problems analytically using the SOV method.

Implement mathematical software (MAPLE) as a problem solving and visualizing tool in tackling BVPs problems.

Solve classical BVPs problems numerically using finite difference schemes.

Conduct, write and present a project carried out independently in a small group related to the BVP at the end of the course.

Realize the significance of the course in real-life problems related to heat and wave in nature.


Year 2007

SYLLABUS CONTENTS

No. Topic

1.0 Introduction Classification of pdes Examples of pde Nondimensionalization

2.0 First order linear pde Analytical methods Numerical methods

3.0 Parabolic equation One dimensional heat equation

- Homogeneous problem- The semi-homogeneous problem- Sturm-Liouville problem

Two dimensional heat flow- Rectangular regions R- The homogeneous case- The semi-homogeneous problem

4.0 Hyperbolic equation – waves in elastic material Strings: 1-D elastic material Membranes: 2-Dimensional elastic material

5.0 The Heat Initial Boundary Value Problem in Polar Coordinates The Laplacian, BC and IC in Polar Coordinates Heat IVBP and homogeneous problem for a disk Heat equation and homogeneous problem for an annulus BVPs in Polar Coordinates

6.0 Finite difference numerical methods First and second order equations in two dimensions.

Methods of Instruction

The course will be conducted through formal, structured lectures, with class time allotted for questions and discussions. There will be a three-hour lecture and one hour tutorial/ computer laboratory session each week.


Year 2007

Assessment

Continuous Assessment : 50% Final Examination (3 hours) : 50%

Total : 100%

References

1. Zill, D.G. & Cullen, M. R. 2005. Differential Equations with Boundary Value Problems. 6th.Edition. Thomson Brooks/Cole.

2. Boyce, E.W., DiPrima, R.C. 2002. Elementary Differential Equations and Boundary Value Problems. 7th. Edition. John Wiley & Sons, Inc.

3. Constanda, C. 2002. Solution Techniques for Elementary Partial Differential Equations. Chapman and Hall.

4. Keane, M.K. 2002. A Very Applied First Course in PDE. Prentice Hall.

5. Kreyszig, E. 2006. Advanced Engineering Mathematics. .John Wiley & Sons Inc.

6. Farlow, S.J. 1982. Partial Differential Equations for Scientists & Engineers. John Wiley & Sons Inc.

7. Smith, G.D. 1985. Numerical Solution of Partial Differential Equations: Finite Difference Methods.3rd Edition. Clarendon Press Oxford.


Year 2007

Syllabus(Mat612) Obe

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