# MATHEMATICS 2 - 2019/0

Module code: ENG1085

Module Overview

Engineers frequently use mathematical models, and in particular differential equations in one or more variables and matrices are common in this context. This is a further first level engineering mathematics module designed to support teaching in other engineering science modules by introducing students to concepts and solution methods in these areas.

Module provider

Civil and Environmental Engineering

Module Leader

SZYNISZEWSKI Stefan (Civl Env Eng)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

JACs code: G100

Module cap (Maximum number of students): N/A

Module Availability

Semester 2

Prerequisites / Co-requisites

Normal entry requirements for the degree programmes in Civil Engineering or Chemical and Process Engineering.

Module content

Indicative content includes:

**Matrices, determinants, eigenvalues:**Matrix addition, multiplication, etc., determinants, Cramer's rule. Matrix operations involving transpose, inverse, rank of matrix. Solving systems of equations using matrices, esp. Gaussian elimination. Eigenvalues and eigenvectors; applications to systems of linear differential equations and normal modes.**Ordinary differential equations**: First order, first degree ODE's of separable type and the integrating factor method. Second order ODE's with constant coefficients (complementary solution and particular integrals). Initial and boundary value problems.**Partial differential equations**Introduction to PDE's, separation of variables method using trial solution; outline of the full method**Laplace and Fourier Transforms:**concepts, properties and definition, identification of signal frequencies using Fourier transform, Laplace transforms of common functions, inverse Laplace transform and application to ODEs. Applications to engineering problems.

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Examination | EXAMINATION (2 HOURS) | 60 |

School-timetabled exam/test | MID-TERM TEST (1 HOUR) | 30 |

Coursework | COURSEWORK | 10 |

Alternative Assessment

N/A

Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate their ability to recognise problem types, select appropriate solution methods and carry out various solution techniques.

Thus, the __summative assessment__ for this module consists of:

- Pieces coursework covering the full breadth of topics and techniques taught, with examples, to not only cover ‘standard’ problems but also some modelling.

Learning outcomes 1-4 10%

- Mid-term test covering the topics and techniques taught in the first half of the semester.

Learning outcomes 1-3 30%

- One two-hour examination with problems on topics from across the whole syllabus but inevitably in the time not covering every technique/concept and with some weighting on those areas from later in the module

Learning outcomes 1-7 60%

__Formative assessment and feedback__

Formative ‘assessment’ is a regular ongoing process all semester through work on the tutorial questions. Formative feedback is provided orally on a one-to-one basis and to the whole group in tutorial/problems classes, via uploaded feedback videos and through the issue using the VLE of selected samples of fully worked solutions to tutorial problems.

Formative Coursework #2 covers learning outcomes (LO) 4-6. Submission and a pass are required to get marks for the summative Coursework #1 (LO 1-4).

The summative assessment is also formative, with individual comments on performance being returned along with scripts and also with overview comments posted on the VLE.

Module aims

- Further understanding and knowledge of mathematical and statistical concepts and techniques
- Skills in the selection and implementation of mathematical techniques to engineering problems
- An appreciation of the importance of mathematical modelling of physical problems and the interpretation of mathematical results

Learning outcomes

Attributes Developed | Ref | ||
---|---|---|---|

002 | Manipulate matrices in appropriate contexts and use matrix methods to solve sets of linear algebraic equations | KC | SM2B, SM2M |

003 | Compute invariant properties such as determinant, trace or principal values | KC | SM2B, SM2M |

004 | Determine matrix eigenvalues and eigenvectors, use to solve engineering systems modelled by differential equations and relate the results to characteristics of the physical system | KCP | SM2B, SM2M, EA2 |

005 | Solve straightforward ordinary differential equations as encountered in engineering problems | KCP | SM2B, SM2M |

006 | Solve typical engineering-related second order partial differential equations | KC | SM2B, SM2M, EA3B |

007 | Apply Fourier and Laplace Transforms to engineering problems | KCP | SM2B, SM2M, EA3B |

001 | Discuss the role of mathematical modelling and be able to produce and explain simple mathematical models of physical problems. | CPT | SM2B, SM2M, B |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Overall student workload

Independent Study Hours: 95

Lecture Hours: 44

Tutorial Hours: 11

Methods of Teaching / Learning

The __learning and teaching__ strategy is designed to familiarise students with mathematical concepts and techniques, supported by extensive use of examples and applications, in which students themselves are engaged in both lectures and, more extensively, in tutorials/problems classes.

The __learning and teaching__ methods include:

- Lectures (4 hrs/wk, for 11 weeks) to introduce new concepts and techniques and provide illustrative examples and applications; students are engaged with performance of examples, questioning on concept and observations.
- Recommended wider reading of matching sections of relevant recommended texts.
- Problem sheets of examples for technique selection and skill development.
- Tutorials/problems classes (1 hr/wk for 11 weeks) with staff and PG assistance for the development of skills in technique application and also in selection of appropriate techniques, using the above problems sheets; assistance is given both at individual level, and for the group on common areas of difficulty
- Coursework (summative but also formative) to assess technique selection and skill development and also elements of modelling and interpretation of physical problems
- Examination

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Chemical and Petroleum Engineering BEng (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Chemical Engineering BEng (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Civil Engineering BEng (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Chemical Engineering MEng | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Chemical and Petroleum Engineering MEng | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Civil Engineering MEng | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2019/0 academic year.