SMA3116 Course Outline

7/21/2019 SMA3116 Course Outline

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NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY

Faculty of Applied Sciences

Department of Applied Mathematics

Semester I 2012/2013

SMA 3116 Engineering Mathematics IV

Lecturer: Mr H. Nare

Course Pre-requisites: SMA1116, SMA1216, SMA2116

Lecture times: Tue & Fri 13:00 to 15:00 Hrs

Course outline

Description

This course introduces engineering students to partial differential equations, their solution

using the method of separation of variables, to the power series solution of ordinary

differential equations and to special functions, and to numerical methods for equation

solution, curve fitting, differentiation, integration and the solution of ordinary differentialequations.

Performance objectives

On completion of the course students should be able to:

- solve simple partial differential equations by direct integration or by the use of thetechniques of ordinary differential equations

- solve eigenvalue and eigenfunction problems that arise in simple boundary value

problems- use the method of separation of variables to solve boundary value problems with

the Laplace, Diffusion and Wave equations

- use the power series method to solve ordinary differential equations in theneighbourhood of an ordinary point

- identify and classify the singular points of an ordinary differential equation

- use the method of Frobenius to solve ordinary differential equations in the

neighbourhood of an regular singular point- solve Bessel’s equation and others to identify a solution as a particular special

function

- understand the concept of different types of error encountered in numerical

methods- understand and use a variety of methods, including iteration and Newton’s, to find

the roots of an equation

- understand and use a variety of methods to fit a curve to a set of points



- understand and use a variety of methods, including the Three Point Method, to

differentiate a function of one variable

- understand and use a variety of methods, including Simpson’s rule, to evaluate

definite integrals

Course Outline

Chapter OneOrdinary Differential Equations (6 Lectures)

Power series solutions

Singular points

Frobenius method

Special functions and their properties

Legendre polynomials

Bessel functions

Chapter TwoPartial Differential Equations (3 Lectures)

Solution of partial differential equations

The wave equation

The one dimensional heat flow problem

Method of separation of variables

Chapter Three

Numerical Methods (11 Lectures)

Errors, relative and absolute

The solution of non-linear equations

The solution of linear systems Interpolation and polynomial approximation

Curve fitting

Numerical differentiation and integration

Approximate solution of differential equations

Test One-Chapter One and Two

Test Two-Chapter Three

Assessment

Coursework: 25%, via 2 tests – one on Partial Differential Equations and Power Seriesmethods, the other on numerical methods and two assignments.

Examination: 75%. A compulsory Section A of 40 marks, with a choice of questions in

Section B – of which 3 should be answered contributing 20 marks each.



Text Books

1. Boyce W.E., and DiPrima R.C. (2004). Elementary Differentrial Equations and

Boundary Value Problems. Eighth edition. John Wiley and Sons.

2. Burden R.L., and Douglas Faires L. (2000). Numerical Analysis. 7th Edition.

Brooks Cole.

3. DiBenedetto E. (2009). Partial Differential Equations. 2nd Edition. Birkhauser

Boston.

4. Drabek P., and Holubova G. (2007). Elements of Partial Differential Equations.

Walter de Gruyter, Boston and New York.

5. Edwards H., and Penney D. (2004). Elementary Differential Equations withBoundary Value Problems. Prentice-Hall, Inc.

6. O’Neil P.V.

(2008). Beginning Partial Differential Equations. 2

nd

Edition. JohnWiley and Sons.

7. Tennenbaum M., and Pollard H. (1985). Ordinary Differential Equations.

Dover Publications.

SMA3116 Course Outline

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