Advanced Mathematics and Statistics for Mechanical Engineers
| Code | School | Level | Credits | Semesters |
| MATH2045 | School of Mathematical Sciences | 2 | 10 | Autumn China |
- Code
- MATH2045
- School
- School of Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Autumn China
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;
- Homogeneous and inhomogeneous second-order ODEs;
- Fourier series and their application to ODEs;
- Laplace transform and its application to ODEs;
- Separation of Variable Technique for PDEs;
- Discrete and continuous probability distribution;
- Design of experiments;
- Variance and error analysis.
Target Students
BSc, 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 2 lecture hours 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: Problems-based assignment
- 90% Exam (2-hour): 2-hour written examination
Assessed by end of autumn semester
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 an introduction to probability and statistics, and to apply statistical methods to the analysis of experimental data.Learning Outcomes
Knowledge and understanding of mathematics necessary to support application of key engineering principles. To apply mathematical methods, tools and notations proficiently in the analysis and solution of engineering problems.
On successful completion of this module students will be able to:
- L01 – Understand concepts of complex numbers, and apply them to solving polynomial equations.
- L02 – Solve a range of linear second-order ordinary differential equations.
- L03 - Understand and calculate the representation of a periodic function by a Fourier Series and use Fourier Series in solving differential equations.
- L04 – Solve linear differential equations using Laplace transforms and their inverses.
- L05 - Apply separation of variables to relevant partial differential equations.
- L06 – Formulate and use the most important probabilistic models used in engineering situations.
- L07 – Apply statistical methods to the design and analysis of experiments.