MAU33E01 Engineering mathematics V
| Module Code | MAU33E01 |
|---|---|
| Module Title | Engineering mathematics V |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Pierre-Yves Bienvenu |
| Module Prerequisites | MAU22E02 Engineering mathematics IV |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 20% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures and 1 tutorial per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Calculate the coefficients of the Fourier series for a variety of functions and use them to solve various differential equations.
- Calculate the Fourier transforms of simple functions and apply the Fourier transform to solve the heat and wave equations over infinite domains.
- Solve the heat, wave and Laplace equations, subject to various boundary conditions, using either separation of variables or Fourier methods.
- Solve linear optimization problems using the simplex and two-phase simplex methods.
- Find the dual of a given linear programming problem and use the duality theorems to solve it.
Module Content
- Fourier methods: definition of complex and real Fourier series, applying Fourier series to solve ordinary differential equations, even and odd half-range expansions, Fourier transform, interpretation of Fourier modes as frequencies, convolution.
- Partial differential equations: Laplace equation, heat equation, wave equation, D'Alembert's solution, fundamental solution, separation of variables, applying Fourier analysis to initial value problems.
- Probability and statistics: basic probability, random variables, discrete and continuous distributions, descriptive and inferential statisticsm sample theory, confidence intervals, null hypothesis.
Recommended Reading
- Advanced engineering mathematics by Erwin Kreyszig.