# MATHEMATICS 1 - 2021/2

Module code: ENG1084

## Module Overview

A first level engineering mathematics module designed to briefly revise and then extend A-Level maths material and introduce more mathematical techniques to support engineering science modules.

### Module provider

Sustainability, Civil & Env Engineering

### Module Leader

ASTON Philip (Physics)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 4

### JACs code: G100

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

## Overall student workload

Independent Learning Hours: 84

Tutorial Hours: 11

Guided Learning: 33

Captured Content: 22

## Module Availability

Semester 1

## Prerequisites / Co-requisites

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

## Module content

Indicative content includes:

**Functions:** Briefly revise the concept of a function; domain, range. Odd, even and periodic functions. Trig functions. Hyperbolic functions. Exponential and logarithmic functions and their graphs. Inverse functions. Algorithms. Numerical methods. Series and limits. Examples with engineering context.

**Differentiation**: Briefly revise the concept of derivative and rules of differentiation for a function of one variable. Applications to gradients, tangents and normals, extreme points and curve sketching, Taylor and Maclaurin series. Formulating differential equations. Functions of several variables: partial derivatives for functions of several variables, total derivative, application to small changes in a function and errors. Extrema of functions of two variables. Examples with engineering context.

**Integration**: Briefly revise the concept of indefinite integration as the inverse of differentiation and standard methods for integration such as substitution, integration by parts and integration of rational functions. Definite integration, area under curves, use of recurrence relationships. Applications of integration to curve lengths, surfaces and volumes of revolution, first moments and centroids, second moments and radii of gyration. Simple double integrals.

**Probability and ****Statistics**: descriptive statistics: numerical (mean, mode, median, variance etc) and graphical summaries. Basic probability: elementary laws, random variables, mean and variance. discrete probability distributions (binomial, Poisson); continuous probability distributions (normal). Statistics with Matlab.

**Mechanics:** Vectors as quantities with magnitude and direction, graphical representation, addition and subtraction, unit vectors, scalar (dot) product, projection, resolution into components; cross (vector) product. SUVAT equations.

**Complex numbers**: Real and imaginary parts, polar form, Argand diagram, exp(jx), De Moivre’s theorem and applications.

## Assessment pattern

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

Online Scheduled Summative Class Test | ONLINE IN SEMESTER TEST (50 MINS) | 30 |

Examination Online | ONLINE 24 HOUR (OPEN BOOK) EXAM | 70 |

## Alternative Assessment

None

## Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate their knowledge of mathematical concepts and rules, and to show their skills in solving mathematical and engineering problems using appropriately selected techniques. The coursework will have two elements. One of these will be a timed class test, covering simpler material and with shorter questions where the final answer is the critical factor; this test may be computer based. The other element will be a coursework assignment with longer, more complex questions where the method as well as a final answer is important.

Thus, the __summative assessment__ for this module consists of:

Examination [Learning outcomes 1-6] 2 hrs 70%

In semester test [Learning outcomes 1,2,3,4] 20%

Coursework assignment [Learning outcomes 4,5,6] 10%

__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, and through the issue using the VLE of fully worked solutions to tutorial problems some time after the class.

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

- Consolidate and extend students' knowledge of basic mathematical concepts and techniques relevant to the solution of engineering problems
- Make students aware of possible pitfalls
- Enable students to select appropriate methods of solution
- Enable students to apply their mathematical knowledge and skills to engineering problems

## Learning outcomes

Attributes Developed | |||

Ref | |||
---|---|---|---|

001 | Manipulation of standard functions | KCPT | SM2B |

002 | Use of the techniques of differential and integral calculus for functions of one and two variables | KCPT | SM2B |

003 | Application of differentiation and integration to determine physical engineering properties | KCPT | SM2B |

004 | Calculation of probabilities and summary statistics. | KCPT | SM2B |

005 | Use of vector algebra and applications of this to mechanics | KCPT | SM2B |

006 | Use of complex numbers | KCPT | SM2B |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## 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; students themselves are engaged in the solution of problems and application of techniques in tutorials/problems classes.

The __learning and teaching__ methods include:

- Lectures (4 hrs/wk for 10 weeks, 2 hrs/wk for 1 week) to revise underpinning prior learning and bring students from varying background to a common level of knowledge, and to introduce new concepts and techniques and provide illustrative examples and applications.
- Labs (2 hrs/wk for 1 week) to introduce Matlab as a tool for performing calculations in Statistics.
- 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
- 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.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **ENG1084**

## Programmes this module appears in

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

Civil Engineering BEng (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Civil Engineering MEng | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Chemical and Petroleum Engineering BEng (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Chemical Engineering BEng (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Chemical and Petroleum Engineering MEng | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Chemical Engineering MEng | 1 | 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 2021/2 academic year.