Course Details in 2020/21 Session
|Module Title ||Engineering Mathematics 3|
|School||School of Engineering|
|Department || Mechanical Engineering|
|Module Code || 04 23779 |
|Module Lead ||Dr Daniel Loghin|
|Level || Honours Level |
|Credits || 20 |
|Semester|| Semester 2|
|Restrictions || None |
Guided independent study-140 hours
Supervised time in studio/workshop-10 hours
Total: 200 hours
|Exclusions || |
|Description || The aim of the module is to enhance the students’ mathematical knowledge and confidence in preparation for the demanding applications of the final stage modules, and a possible research career involving engineering science. They will develop an understanding of the numerical techniques used within modern Finite Element Analysis computer packages and develop an understanding of the mathematical basis of many of the advanced systems of equations governing engineering problems.|
1. Vector differential calculus:
- review of vectors and geometry;
- review of grad, div, curl;
- calculus for parametrised fields;
- applications: PDE of physics and engineering.
2. Vector integral calculus:
- line, surface, volume integrals
- Stokes’ theorem and Gauss’ divergence theorem;
- integro-differential identities;
- applications: length, area, volume, mass, conservation laws.
3. Numerical methods:
- Nonlinear iterations with application to root-finding methods:
- fixed point iteration method;
- secant and Newton's method;
- interpolation by polynomials:
- Lagrange and Hermite interpolation;
- piecewise polynomial interpolation;
- numerical methods for initial value problems
- explicit Runge-Kutta methods.
|Learning Outcomes || By the end of the module the student should be able to:|
Demonstrate knowledge and understanding of a wide range of standard numerical techniques employed in mechanical and related engineering disciplines.
- Demonstrate proficiency in vector calculus, including a good understanding of 3D geometry, ability to evaluate line, surface and volume integrals as well as the ability to solve boundary value problems using some standard techniques.
23779-05 : Exam : Exam (Centrally Timetabled) - Written Unseen (85%)
23779-20 : Semester 1 : Class Test (7.5%)
23779-21 : Semester 2 : Class Test (7.5%)
|Assessment Methods & Exceptions || Assessments:|
(100%) Continuous assessment (comprising two timed summative assessments, 50% each). (The final 50%: replaced by 2-hour closed book centrally timetabled exam in May/June assessment period if this is possible).
|Other || None|