Advanced Mathematics and Statistics for Mechanical Engineers
| Code | School | Level | Credits | Semesters |
| MATH2043 | Mathematical Sciences | 2 | 10 | Autumn Malaysia |
- Code
- MATH2043
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Autumn Malaysia
Summary
The module covers advanced methods for second order differential equations, with particular focus on equations that occur in engineering contexts. The statistics part will focus on analysis of experimental data.
· Complex numbers (Revision) (Week 3)
· Homogeneous and inhomogeneous second-order ODEs; (Week 3-4)
· Fourier series and their application to ODEs; (Week 5-7)
· Laplace transform and its application to ODEs; (Week 8-10)
· Separation of variable technique for PDEs; (Week 11-12)
· Discrete and continuous probability distribution; (Week 13)
· Design of experiments; (Week 13-14)
· Variance and error analysis. (Week 14)
Target Students
BEng and MEng students in the Department of Mechanical, Materials and Manufacturing Engineering
Classes
- One 1-hour workshop each week for 12 weeks
- One 2-hour lecture each week for 12 weeks
Each week there will normally be a 2-hr lecture to introduce key mathematical knowledge/ideas/techniques on module topics, and 1 hr problem class to provide students with the opportunity to gain individual help understanding module topics, clarification of lecture notes or support in developing problem solving skills.
Assessment
- 10% Coursework: 1 hr inclass test
- 90% Exam (2-hour): 2- hour written exam
Educational Aims
To understand fundamental concepts of complex numbers, in particular to apply them to solutions of polynomial equations. To understand, apply and manipulate standard techniques for solving important classes of ordinary differential equations and the calculus relevant to analysing core engineering models. Fundamental concepts for solving partial differential equations relevant to modelling of thermodynamic, fluid or elastic problems are introduced and illustrated by obtaining fundamental solutions using techniques developed within the module. To provide and introduction to probability and statistics, and to apply statistical methods to the analysis of experimental data.Learning Outcomes
On successful completion of this module students will be able to:
LO1: Understand the properties and characteristics of extended concepts: complex number for solving polynomials, linear differential equations, Fourier series, Laplace transforms, relevant partial differential equations and relevant probabilities models. AHEP4:M1, M3; EAC:PO1, PO5
LO2: Apply these techniques in the manipulation and solution of mathematical problems. AHEP4: M1, M2; EAC:PO1, PO2
LO3: Apply these techniques in the solution to the simple engineering problems, and statistical analysis of experiments. AHEP4:M2; EAC:PO2
Conveners
- Dr Yee Jiun Yap