MATHEMATICS 2 - 2021/2

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. Statistics and probability also play a significant role in the assessment of real-life engineering problems and an introduction to key concepts in this area is also included

Module provider

Mechanical Engineering Sciences

Module Leader

KUEH Audrey (Physics)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

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

Module Availability

Semester 2

Prerequisites / Co-requisites

ENG1061 Mathematics 1

Module content

Indicative content includes:

• 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. Simple double integrals. Simple vector functions of several variables and basic vector calculus- grad, div and curl


• 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.


• 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.


• Partial differential equations Introduction to PDE's, separation of variables method using trial solution.


• Probability and statistics:  Descriptive statistics: numerical (mean, mode, median, variance etc)..  Basic Probability: elementary laws, random variables, mean and variance. Probability distributions: Discrete probability distributions (binomial, Poisson); continuous probability distributions (normal). 

Assessment pattern

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:

• One piece of coursework covering the full breadth of topics and techniques taught in the first part of the semester, with examples to not only cover ‘standard’ problems but also some modelling.

Learning outcomes 1,2,3           20%         12 hrs           

• 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 1,2 ,4-8       80%        2 hrs

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 selected samples of fully worked solutions to tutorial problems.

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

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 intepration 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.

Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: ENG1065

Programmes this module appears in

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.