OBE-2: Syllabus
Code : MAT565
Course : Advance Differential Equations
Level : Bachelor
Credit Unit : 3
Contact Hour : 4 (3 hr. Lecture, 1 hr. Tutorial)
Part : 6
Course Status : Non-Core
Prerequisite : Further Calculus for Engineers
Course Outcomes : After completing this course, the students should be able to:
Determine Laplace transforms of functions using definition and
properties.
Apply inverse Laplace transform to solve differential equations.
Express any periodic function in a Fourier series form.
Solve partial differential equations using separable variables
method.
Course Description : This course consists of Laplace transforms, systems of linear first-
order differential equations, Fourier series and boundary value
problems. The students will learn how to express any periodic function
in a Fourier series form. The students will also learn Laplace transform
as a tool to solve ordinary differential equations and system of first and
second order differential equations. The last chapter is to solve the
boundary value problems using the method of separation of variables
and Fourier series.
Syllabus Content : Laplace Transform
Definition and transformation of basic functions
Properties of Laplace Transform
Inverse of Laplace transform
Solution of differential equations using Laplace Transform
Solution to system of linear differential equations.
Fourier Series
Periodic functions
Odd and even functions
Expansion of periodic function in Fourier series
Fourier Sine and Cosine series
Harmonic analysis
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OBE-2: Syllabus
Partial Differential Equations and Boundary Value Problems
Introduction to PDE and method of separation of variables
Boundary value problems.
Wave Equations
Teaching : A combination of any of the following methods:
Methodology Lectures
Tutorials
Assessment : Final examination – One 3-hour paper : 60%
Course Work: : 40%
Test 1 – 10%
Test 2 – 10%
Test 3 – 10%
Quizzes(3) – 10%
Text : A.C. Srivastava and P.K. Srivastava (2011). Engineering Mathematics
Volume II, PHI.
References : 1. Boyce, W.E., & DiPrima, R.C., Elementary Differential Equations,
7th edition, John Wiley & Sons Ltd,2000
2. Kreyzig. E., Advanced Engineering Mathematics, 8th edition, John
Wiley & Sons Ltd, 1998
3. Nagle, Kant R. & Staff, Edward B., Fundamentals of Differential
Equations and Boundary Value Problems, 2nd Edition, Addison-
Wesley Publishing Company, 1996.
4. Spiegel, Murray R., Schaum’s Outline of Theory and Problems of
Fourier Analysis with Applications to Boundary Value Problems,
McGraw-Hill Book Company.
5. Strauss, W. A., Partial Differential Equations: An Introduction,
John Wiley & Sons Ltd, 1992
6. Zill, Dennis G., Cullen, Michael R., Differential Equations with
Boundary-Value Problems, 8th Edition, Brooks/Cole Thomson
Learning, 2012.
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OBE-2: Syllabus
Scheme Of Work March 2018-Julai 2018
No. of
Week Date Topic and Sub-topic Remarks
Hours
Laplace Transformation
3 Entrance
1 Definition and transformation of basic functions.
5 - 9 Mac Survey
1
Tutorial
Properties of Laplace transform:
Entrance
2 i) Linearity 3
12 - 16 Mac Survey
ii) First shifting
n
iii) Multiplications by t
Tutorial 1
iv) Second Shifting
3.
v) Transformation for differential and integral
3 19 – 23 Mac
functions
Tutorial 1
Inverse Laplace Transform
3
4 i) Properties
26 - 30 Mac
Tutorial
1
Quiz 1
3
ii) Partial Fractions
5
2 - 6 Apr iii) Convolution
Tutorial 1
2
Solution of Differential Equations
6 9 - 13 Apr
1
TEST 1
Tutorial 1
SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS
3
7 Introduction
16 - 20 Apr Review of Cramer’s Rule ( Matrix theory )
Solving system of ODE using Laplace Transform.
Tutorial 1
Solving system of ODE using Laplace Transform 3
8 23 – 27 Apr
Tutorial
1
Quiz 2
FOURIER SERIES
Odd, Even and Periodic Functions. Labour Day
30 Apr – 4 3 1 May
9
May Introduction to Fourier Series. Fourier series for : (Tuesday)
i) Simple analytic functions
Tutorial 1
OBE-2: Syllabus
No. of
Week Date Topic and Sub-topic Remarks
Hours
ii) Wave functions
iii) Triangular functions 2 SUFO
TEST 2 7 May – 14 Jun
10 7 - 11 May
1
Tutorial
1
Half range
3
Harmonic Analysis
11 14 – 18 May
Tutorial 1
PARTIAL DIFFERENTIAL EQUATIONS and BVP
Introduction 3
12 21 – 25 May
Tutorial
TEST 3
Wesak
Mid-Semester Break 29 May
28 May – 3 (Tuesday)
Jun Gawai
30 - 31 May
Boundary Value Problem ( BVP)
2
13
Exit Survey
4 - 8 Jun Tutorial 1
Quiz 3 1
14 Wave Equation 3
11 - 15 Jun Exit Survey
Tutorial 1
Hari Raya
15 - 21 Jun Revision Week
15 – 16 Jun
22 Jun- 15 July Final Examination 3 Week
