# MATHEMATICS 1 - 2025/6

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

GRANT James (Maths & Phys)

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

Independent Learning Hours: 84

Lecture Hours: 33

Tutorial Hours: 11

Guided Learning: 11

Captured Content: 11

Semester 1

None

## 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
School-timetabled exam/test IN SEMESTER TEST (50 MINS IN-PERSON INVIGILATED) 30
Examination EXAM (2 HOUR IN-PERSON INVIGILATED) 70

N/A

## 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 summative assessment for this module consists of:

• In semester test [Learning outcomes 1,2,3,4,5]

• Examination  [Learning outcomes 1-6]

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

 Ref Attributes Developed 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 and pre-recorded captured content 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.

• Recommended wider reading of matching sections of relevant recommended texts.

• Problem sheets of examples for technique selection and skill development.

• Tutorials/problems classes 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

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.

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

## Other information

Surrey's Curriculum Framework is committed to developing graduates with strengths in Employability, Digital Capabilities, Global and Cultural Capabilities, Sustainability and Resourcefulness and Resilience. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

Digital capabilities: Students are expected to engage with online material and resources via SurreyLearn and encouraged to communicate with one another through the discussion forums created and the self-study questions that have been developed for them. The exam is administered online too.

Resourcefulness and Resilience: Students develop experience in applying new learned skills and knowledge to solve problems.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
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
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 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 2025/6 academic year.