Module Catalogue

MEC2101 : Numerical and Analytical Methods A

  • Offered for Year: 2017/18
  • Module Leader(s): Dr Kheng-Lim Goh
  • Owning School: Mechanical & Systems Engineering
  • Teaching Location: Singapore
Semesters
Semester 1 Credit Value: 10
Semester 2 Credit Value: 10
ECTS Credits: 10.0

Aims

For students who have studied engineering mathematics previously, to develop aware and confident users of numerical and analytical tools for:
-       introduction to mathematical modelling;
-       statistical methods for process control;
-       ordinary differential equation modelling;
-       operational research.

Outline Of Syllabus

1.       Introduction to mathematical modelling:
- Problem solving: expressing simple mathematical models eg ODE's, through software.
Introduction to optimization problems – linear programming.

2. Statistical methods for process control:
- Data Properties: probability, distributions, descriptive statistics, data
sampling and evaluation
- Statistical Inference: sampling distributions, confidence interval, measurement uncertainty
and manufacturing tolerancing, one and two sample problems.
- Regression analysis and ANOVA.

3. Vibration and control system analysis:
- Systems of linear equations (eigenvalues and eigenvectors).
- Phase-plane and stability (self-excitation).
- Laplace Transforms,Fourier series.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion11:301:30End of Semester 2 Exam
Guided Independent StudyAssessment preparation and completion11:001:00End of Semester 1 Exam
Guided Independent StudyAssessment preparation and completion47:3030:00Target non-timetable hours to complete coursework assignment submissions
Guided Independent StudyAssessment preparation and completion400:3020:00Recommended revision for exams, assuming prior regular independent study throughout teaching
Scheduled Learning And Teaching ActivitiesLecture741:0074:00Structured presentation of syllabus may include skills demonstration, formative feedback, etc
Guided Independent StudyIndependent study113:3013:30Recommended regular personal study throughout teaching period to follow up taught classes
Guided Independent StudyIndependent study203:0060:00Unsupported computer time.
Total200:00
Teaching Rationale And Relationship

Lectures:
-       convey the underlying mathematical principles
-       illustrate engineering applications of these, and
-       brief the software-based case-study explanations.

Workshops provide support for the case-study initial modelling, model software implementation and model application phases.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination601A20Vibration and control: Introduction to modelling.
Written Examination902A30Statistical methods: Operational Research.
Other Assessment
Description Semester When Set Percentage Comment
Report2M20Statistical methods project (max 7.5 hours)
Report1M15Vibration and control project (max 7.5 hours), or quiz.
Report2M5Operational research project (max 7.5 hours).
Report1M10Mathematical modelling project (max 7.5 hours).
Assessment Rationale And Relationship

This module focus is on building awareness and confidence in the use of mathematical and statistical tools embodied in proprietory software, so all assessment is by a series of software-based case-study assignments addressing typical manufacturing engineering problems.

Reading Lists

Timetable