MATHEMATICS 2 - 2024/5

Module code: ENG1065

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

KUEH Audrey (Maths & Phys)

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

Independent Learning Hours: 73

Lecture Hours: 33

Tutorial Hours: 11

Captured Content: 33

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

Assessment type Unit of assessment Weighting
School-timetabled exam/test TEST (1 hr duration) 20
Examination EXAM (2 hrs duration) 80

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.

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.

Summative assessment

Summative assessment is in the form of an online class test and a final examination

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

 Attributes Developed 001 Select and apply appropriate techniques of differential and integral calculus to engineering problems; KC 002 Solve straightforward ordinary differential equations as encountered in engineering problems; KCP 003 Discuss the role of mathematical modelling and be able to produce and explain simple mathematical models of physical problems; CPT 004 Solve typical engineering-related second order partial differential equations; KC 005 Manipulate matrices in appropriate contexts and use matrix methods to solve sets of linear algebraic equations; KC 006 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 007 Present and summarise simple statistical data graphically and numerically; KCPT 008 Recognise appropriate probability distributions and use them to calculate probabilities and apply to e.g. simple ideas of quality control. 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, in which students themselves are engaged in both lectures and, more  extensively, in tutorials/problems classes.

The learning and teaching methods include:

• Lectures (3 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

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.