# MATHEMATICS I: PURE MATHEMATICS - 2020/1

Module code: EEE1031

Module Overview

Expected prior learning**:** Mathematical knowledge at the level of entry requirements for a degree programme in Engineering.

Module purpose:** **Mathematics is the best tool we have for quantitative understanding of engineering systems. This course in pure mathematics is specifically designed for Electronic Engineering students and covers the fundamental techniques for many future engineering courses taught here.

Module provider

Electrical and Electronic Engineering

Module Leader

PRINSLOO Andrea (Maths)

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 1

Prerequisites / Co-requisites

None.

Module content

The following topics will be taught:

**Algebra:** Basic algebra (factorisation, partial fractions, roots of quadratics and other simple equations, linear simultaneous equations), geometry, trigonometry. Trigonometric identities and solutions of trigonometric equations.

**Properties of Functions:** Exponential and logarithmic functions and their properties. Odd, even and periodic functions. Concept of a function and inverse functions, trigonometric and inverse trigonometric functions, solution of trigonometric equations.

**Complex numbers:** real and imaginary parts, polar and exponential form, Argand diagram, exp(jx) = cos x + j sin x, relationships between trigonometric functions, De Moivre’s theorem and applications.

**Vectors**: Magnitude, dot and cross product. Meaning of the dot and cross product.

**Differentiation:** Concept of derivative and rules of differentiation for a function of one variable. Differentiation of trigonometric, exponential and logarithmic functions. Applications to gradients, tangents and normals, extreme points and curve sketching. Functions of several variables. The idea that the graph of z=f(x,y) is a surface. First and second order partial derivatives and their meanings as slopes in particular directions. The total differential and applications to errors and rates of change.

**Sequences and Series:** Arithmetic and geometric sequences and series. Binomial expansion. Maclaurin and Taylor series expansions. Calculation of approximations and limits using power series. Evaluation of limits, including L'Hôpital's Rule.

**Integration:** 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, areas under curves. Mean and rms values. Integrals requiring trigonometric substitutions. Calculation of areas under curves given implicitly.

**Further Integration:** Evaluation of multiple integrals with both constant and non-constant limits. Interpretation of the region of integration of a multiple integral and evaluation of multiple integrals by changing the order of integration.

**Numerical methods:** Newton-Raphson method; numerical integration using power series.

Assessment pattern

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

School-timetabled exam/test | AN UNSEEN 1-HR WRITTEN CLASS TEST (WEEK 4) | 20 |

School-timetabled exam/test | AN UNSEEN 1-HR WRITTEN CLASS TEST (WEEK 8) | 20 |

Examination | 2 HOUR CLOSED BOOK EXAMINATION | 60 |

Alternative Assessment

Not applicable: students failing a unit of assessment resit the assessment in its original format.

Assessment Strategy

The** assessment strategy** for this module is designed to provide students with the opportunity to demonstrate the learning outcomes. The written examination will assess the knowledge and assimilation of mathematical terminology, notation, concepts and techniques, as well as the ability to work out solutions to previously unseen problems. The in-semester tests give the students a chance to practice the required techniques shortly after they have been taught.

Thus, the **summative assessment** for this module consists of the following:

· 2-hour, closed-book written examination (60%)

· 1-hour unseen written in-semester test (typically in week 4) (20%)

· 1-hour unseen written in-semester test (typically in week 8) (20%)

Any deadlines given here are indicative. For confirmation of exact date and time, please check the Departmental assessment calendar issued to you.

**Formative assessment and feedback **

For the module, students will receive formative assessment/feedback in the following ways:

· During lectures, by question and answer sessions

· During office hour meetings with students

· By means of unassessed tutorial problems in the notes (with answers/model solutions)

Module aims

- This module aims to provide students with some of the basic understanding and skills in mathematics needed to follow a degree prgramme in engineering.

Learning outcomes

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

1 | Demonstrate knowledge of the concepts, notation and terminology introduced in the module | KCT |

2 | Perform basic calculations accurately | CPT |

3 | Solve problems in the key mathematical areas | KCT |

4 | Present solutions in a clear, structured way, with accuracy and logical consistency | KPT |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Overall student workload

Independent Study Hours: 117

Lecture Hours: 51

Methods of Teaching / Learning

**The learning and teaching strategy** is designed to achieve the following aims:

Student familiarity with the basic concepts, notations and techniques used in mathematics as it is applied to engineering.

Facility with the underlying mathematical tools that will support many other courses in the Electronic Engineering degree programmes.

All students should be at a sufficient level of ability in Mathematics by the end of semester 1 that they can benefit from the course Mathematics II – Applied Mathematics.

**Learning and teaching methods**include the following.

Lectures (3 or 5 hours per week for 11 weeks, depending on stream)

Class discussion in lectures

One-to-one sessions with lecturers during office hours.

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

Reading list for MATHEMATICS I: PURE MATHEMATICS : http://aspire.surrey.ac.uk/modules/eee1031

Programmes this module appears in

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

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

Electronic Engineering with Computer Systems MEng | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

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

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

Electronic Engineering with Space Systems MEng | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

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

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

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

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

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

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

Electronic Engineering with Space Systems BEng (Hons) | 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 2020/1 academic year.