Faculty of Science and Engineering
Department Of Mathematics
Course Title
Course Code
Year
Credits
Course type
Prerequisite
course(s)
PARTIAL DIFFERENTIAL EQUATIONS
MAT416
2023/24
Semester
Lecture hours: 3
Core
Required
1st Semester
2nd Semester
Practical hours:01
Elective
Total credit:3.7
General Education
MAT112, MAT212, MAT216
Course Description
This course introduces the learner to partial differential equations (PDEs). It extends the ideas learned in the
ordinary differential equations course to the case when the unknown function depends on more than one variable.
The importance of this course cannot be overemphasized as most problems that arise in applications are governed
by a differential equation. The methods developed in this course are typically analytic in nature. Assessment of the
course is by means of continuous assessment and a 3-hour final examination. The CA to exam ratio is 2:3.
Broad Course objective
The main objective of this course is to expose the learner to how PDEs arise mathematical modeling and equip
them with analytic skills to solve first order and linear second order PDEs.
Course Objectives
At the end of the course, students will be able to:
a. Classify PDEs according to order, linearity and homogeneity
b. Integrate first order PDEs using the method of characteristics
c. Derive the diffusion equation
nd
d. Classify linear 2 order PDEs as parabolic, hyperbolic or elliptic
nd
e. Reduce a linear 2 order PDE into its canonical form
f. Find full-range and half-range Fourier expansions of period functions
g. Solve PDEs using the method of separation of variables
h. Solve PDEs using Laplace transforms
Course content
First Order PDEs. Equations that can be solved by direct integration. The method of characteristics,
particular integral surfaces.
nd
Linear 2 Order PDEs. Mathematical Models. Classification. The Cauchy Problem.
Fourier Series. The full-range series. Half-range series. Parseval’s identity.
Bessel Functions. Identities and recurrence relations
Method of Separation of Variables. Homogeneous problems. Nonhomogeneous problems. Problems
with circular symmetry.
Laplace Transforms. Properties. Solution of PDEs.
Teaching method and activities
Lecture (Blended Learning)
During the lectures, concepts will be introduced and important results derived, after which relevant examples
shall be worked out in detail.
Problem Sets
At the end of each chapter, learners will be given a problem set for more extensive practice.
Tutorial Practicals
At the end of each chapter, learners will be given the opportunity to discuss their solutions to the problem sets
with the instructor.
Assessment method
I. Continuous Assessment
Description
The average of the Quizzes will contribute 10%
towards your CA.
The average of the Assignments will contribute
5% towards your CA.
The average of the Tests will contribute 85%
towards your CA.
Weight (%)
(40%)
Tentative Test Dates: 28 March, 02 May, 23 May
II. Final Exam
A 3-hour exam with 2 sections. A compulsory
Section A, worth 40%, is designed to test basic
understanding of all the topics. Then section B
tests deeper understanding and consists of five
questions. A candidate must answer any 3
questions (worth 20% each) from this section.
(60%)
Prescribed Textbook
JS Mathunjwa Introduction to Partial Differential Equations with Fourier Series and Laplace Transforms, 2024
0
