Differential Equations and Fourier Analysis
| Code | School | Level | Credits | Semesters |
| MATH2034 | School of Mathematical Sciences | 2 | 10 | Spring China |
- Code
- MATH2034
- School
- School of Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Spring China
Summary
This module is an introduction to Fourier series and integral transforms and to methods of solving some standard ordinary and partial differential equations which occur in applied mathematics and mathematical physics. The module describes the solution of ordinary differential equations using series and introduces Fourier series and Fourier and Laplace transforms, with applications to differential equations and signal analysis. Standard examples of partial differential equations are introduced and solution using separation of variables is discussed. The course covers material fundamental to applied mathematics modules at levels 2, 3 and 4.
Target Students
Single Honours and Joint Honours students from the School of Mathematical Sciences. Mathematical Physics Students. Available to JYA/Erasmus students.
Classes
- One 1-hour workshop each week for 12 weeks
- One 2-hour lecture each week for 12 weeks
Activities may take place every teaching week of the Semester or only in certain weeks.
Assessment
- 10% Inclass Exam 1 (Written): Inclass test
- 90% Exam 1 (2-hour): 2-hour written examination
Assessed by end of spring semester
Educational Aims
Thiscourse aims to introduce standard methods of solution for linear ordinary and partial differential equations and to introduce the idea and practice of Fourier series and integral transforms. The mathematical methods taught in this module find wide application across a range of coursesin applied mathematics.Learning Outcomes
A student who completes this module successfully will be able to:
L1 - Classify differential equations and identify suitable methods of solution;
L2 - Solve linear ordinary differential equations by Series Solution and the Frobenius method;
L3 - Compute the Fourier Series of a periodic function and solve aperiodically driven ordinary differential equations with constant coefficients;
L4 - solve the heat and wave equation in one spatial variable using separation of variables;
L5 - solve the two dimensional Laplace equation using separation of variables in cartesian, polar and spherical polar co-ordinates;
L6 - solve linear partial differential equations using the Fourier and Laplace transforms.