EM514: Partial Differential Equations

Basic Details:

Course Code: EM 514
Credits: 2
Pre-requisites: EM211, EM212
Compulsory/Optional: Optional

Aim :

To provide students with the basic understanding of the theory and methods of solutions for partial differential equations.

Intended Learning Outcomes:

On successful completion of the course, the students should be able to ;

Solve first order partial differential equations using the method of characteristics.
Classify linear second order linear partial differential equations and solve them using method of separation of variables and Eigen-function expansion method.

Couse Content:

Introduction

Partial differential equations as a mathematical model and their solutions, initial and boundary value problems

First order Partial Differential Equations

Linear and quasi-linear partial differential equations, method of characteristics

Fourier series

Introduction.

Second Order Linear Partial Differential Equations

Classification, Separation of variables and Eigen-function expansion method,
Examples from the heat, wave, Laplace and Poisson equations;
d’Alembert’s solution to the wave equation.

Partial differential equations in other coordinates

Polar, cylindrical and spherical coordinates.

Numerical solutions of partial differential equations

Finite difference methods.

Time Allocation (Hours):

Lectures

Assignments

Tutorials

Recommended Texts:

Walter A. Strauss, “Partial Differential Equations”, 2nd edition (2008), John Wiley and Sons.
Y.Pinchover and J. Rubinstein, “An Introduction to Partial Differential Equations”, (2005), Cambridge University Press.
P. J. Olver, “Introduction to Partial Differential Equations,”, 3rd edition (2014), Springer.

Assessment:

In - course: