# MATHEMATICS 2 - 2024/5

Module code: ENG1085

## Module Overview

Mathematics is an essential tool which engineers use to understand and solve problems. A good understanding of mathematics is therefore essential for us to tackle the complex problems which our world faces.

This module builds on the foundations learned in ENG1084 – Mathematics 1 and will teach you the mathematical concepts used to describe the physical phenomena which are important for engineering applications. The mathematics covered will also open a window into the extraordinary discoveries of 18th to 20th century physics, ranging from Newtonian mechanics to Einstein’s theory of relativity and quantum mechanics.

You will apply the knowledge of mathematics learned in this module to analyse applied engineering problems, reaching substantiated conclusions from first principles.

### Module provider

Sustainability, Civil & Env Engineering

WALKER Martin (Sust & CEE)

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

Independent Learning Hours: 85

Seminar Hours: 22

Tutorial Hours: 11

Guided Learning: 10

Captured Content: 22

Semester 2

None

## 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.

All topics emphasise applications to engineering problems and encourage the development of critical engineering judgment, resourcefulness, and resilience.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK PART 1 15
Coursework COURSEWORK PART 2 15
Examination EXAM (2-HOUR INVIGILATED IN-PERSON ) 70

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:

• Two pieces of coursework covering most of the topics and techniques taught. These will not only cover standard problems but also some aspects of modelling i.e. mathematically modelling engineering problems. It is an opportunity to practice resourcefulness and resilience in tackling challenging engineering problems. The two pieces of coursework will constitute 30% of the module assessment.

• One two-hour examination covering topics from across the entire syllabus. This will constitute 70% of the assessment.

Formative assessment is a regular ongoing process throughout the semester within work on tutorial questions, seminar activities and lecture examples. Immediate formative feedback is provided during the tutorials, seminars, and lectures.

## Module aims

• Build a working knowledge of the key mathematical techniques relevant for engineering applications
• Develop skills to identify and apply appropriate mathematical techniques to solve engineering problems while recognizing the limitations of these techniques.
• Appreciate the importance of mathematical modelling of physical problems and the interpretation of mathematical results
• Promote mathematical fluency and confidence

## Learning outcomes

 Attributes Developed 002 Manipulate matrices in appropriate contexts and use matrix methods to solve sets of linear algebraic equations KC 003 Compute invariant properties such as determinant and trace KC 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 005 Solve straightforward ordinary differential equations as encountered in engineering problems KCP 007 Solve typical engineering-related second order partial differential equations KC 008 Apply Fourier and Laplace Transforms to engineering problems KCP 001 Discuss the role of mathematical modelling and be able to produce and explain simple mathematical models of physical problems. CPT 006 Solve systems of linear ordinary differential equations KCP

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 will be engaged in lectures, seminars/problems classes, and tutorials.

The learning and teaching methods include:

• Lectures to introduce new concepts and techniques, provide illustrative examples, and explore applications.

• Interactive seminars to reinforce and apply lecture content.

• Computer-laboratory based sessions to understand and solve mathematical problems, helping to develop broadly applicable digital capabilities.

• Problem sheets to practice technique selection and execution and provide skills development. Supported by the tutorials (see below) students will develop confidence and resourcefulness in assessing the correctness of solutions and identifying errors.

• Tutorials/problems classes for individualised and small group guidance and support provided by staff and post graduate students.

• Coursework (summative but also formative) to assess technique selection and skill development, but also gain experience with elements of the mathematical modeling and interpretation of physical problems.

• Recommended wider reading of matching sections of relevant recommended texts and online resources.

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: ENG1085

## Other information

This module addresses the Resourcefulness & Resilience and Digital Capabilities pillars.

Resourcefulness & Resilience: Students will develop the ability to respond to problem-based tasks, addressing challenges or set-backs through agile thinking to provide viable solutions to engineering problems. They are encouraged to exercise and develop their engineering judgement to evaluate solutions and identify and correct errors, learning from this experience to build confidence in their problem-solving abilities .

Digital Capabilities: Students will learn how to use computational tools to understand and solve mathematical problems. They will also appreciate how the mathematics covered in this module underlie specialist engineering tools, such as Finite Element Analysis software. Digital resources to supplement learning will be provided through SurreyLearn, including monitored discussion boards and links to internet-based learning materials.

## 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 and Petroleum Engineering MEng 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
Chemical Engineering MEng 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
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 2024/5 academic year.