MP361 - Ordinary Differential Equations

Lecturer: Prof. Jiri Vala
Address: Room 1.7A, Department of Theoretical Physics, Science Building, North Campus
E-Mail: jiri DOT vala AT mu DOT ie

Lectures:
Tuesdays, 9:05am-9:55am, Hall D, Arts Building
Wednesdays, 9:05pm-9:55pm, JHL 7, Arts Building

Tutor: Mr. Samuel Diabate
Address: Hamilton Institute, Eolas Building, 3rd floor, North Campus
E-Mail: samuel DOT diabate AT mu DOT ie

Tutorials:
Fridays, 11:05pm-11:55pm, Hall B, Arts Building

Content:
This module will be lecture-driven, and the assignments and exam will be based entirely on the material presented in the lectures and tutorials. There is no required textbook for this module; however, the following books might be useful as supplements:

Mary L. Boas, Mathematical Methods in the Physical Sciences (Wiley)
Erwin Kreyszig, Advanced Engineering Mathematics (Wiley)
D. G. Zill, W. S. Wright and M. R. Cullen, Advanced Engineering Mathematics (Jones and Bartlett)

The mathematical background of the students taking this module can vary wildly. To try to address this issue, I include here a link to the notes (written by Charles Nash) for the EE106 module that we teach to the first-year engineers. The vast majority of it is familiar to all of you, but if you feel you need a bit of a reminder as to, say, the basics behind infinite series or what a Taylor series is (both of which will figure into this module), it should serve as a good starting point. Please take the time to go through it.

Assessment:
Your mark for this module will be based on your total continuous assessment mark (20%) and your exam mark (80%). The continuous assessment will consist of problem sets issued (roughly) every week. They will be made available on this webpage (see below) but should be submitted as single scanned PDFs to the module's Moodle page here.

Lecture notes:

Introduction to MP361
Introduction to differential equations
First order ODEs I
First order ODEs II
Introduction to higher-order ODEs
Second-order ODEs: homogeneous equations, method of undetermined parameters
Second-order ODEs: method of variation of parameters
Second-order ODEs: Cauchy-Euler equation
Linear models
Green's function method: Initial value problems
Green's function method: Boundary value problems
Power series solutions of linear differential equations: Introduction
Power series solutions: Ordinary points
Power series solutions: Singular points
Solutions using special functions I: Bessel equation
Solutions using special functions I: Legendre, Laguerre and hypergeometric equations
Laplace transform I: Introduction
Laplace transform II
Laplace transform III
Fourier series and Fourier transform

Homework assignments:
Assignment 1 and the solutions (average mark: )
Assignment 2 and the solutions (average mark: )
Assignment 3 and the solutions (average mark: )
Assignment 4 and the solutions (average mark: )
Assignment 5 and the solutions (average mark: )
Assignment 6 and the solutions (average mark: )
Assignment 7 and the solutions (average mark: )
Assignment 8 and the solutions (average mark: )
Assignment 9 and the solutions (average mark: )
Assignment 10 and the solutions (average mark: )