MEng Mechanical Engineering with Industrial Experience

The course unit aims to provide a second year course in mathematics and statistics.

Evaluate integrals over elementary regions in two and three dimensions as repeated integrals and evaluate certain suitable integrals in three dimensions using cylindrical or spherical polar coordinates.

Define and use the Gradient, Divergence and Curl operators and the directional derivative, together with the geometric interpretation of the Gradient.

Define and evaluate line and surface integrals in three dimensions in certain suitably simple situations.  

State Gauss’s Theorem and Stokes’ Theorem and apply these to find surface integrals in certain suitably simple situations.  

Define the Laplace Transform, highlighting its action on derivatives and integrals, and use this to solve mechanical systems.  

Construct a polynomial interpolant of a function of one variable and see how it can be used to derive composite numerical integration rules.  

Construct a linear least-squares fit of a one-dimensional set of data.  

Distinguish between discrete and continuous random variables and compute summary statistics (mean and variance).  

Compute probabilities of events by modelling uncertain phenomena using uniform, Poisson, exponential and normal distributions.  

Appreciate the implications of the central limit theorem (without seeing a proof).  

Construct confidence intervals and correctly interpret the role that they play in two-sided hypotheses. 

Multiple and Line Integrals. Construction and evaluation of double integrals including changing the order of the integrations.  Change of variable including the Jacobian. Introduction to triple integrals. Further Line integrals.  

Vector Calculus. Scalar and Vector fields. Gradient, divergence and curl. Laplacian. Identities. Line and Surface integrals involving vectors. Vector integral theorems.

Laplace Transforms: Definition. Transforms and Inverse Transforms of Simple Functions. Transforms of derivatives and integrals. Convolution, Solution of Ordinary Differential Equations using Laplace Transforms.

Numerical Methods. Interpolation and Least Squares approximation. Further numerical integration, integration rules, numerical integration where interval or function becomes infinite. Solution of systems of non-linear algebraic equations.

General notion of a random variable, including its definition and the range space. 
Discrete random variables – definition and explanation;  probability mass function (pmf);  discrete Uniform distribution;  Binomial distribution;  mean and variance of discrete random variables. 
Continuous random variables – definition and explanation; probability density function (pdf);  Uniform distribution;  Exponential distribution;  Normal distribution;  mean and variance of continuous random variables. 
Linear transformations of random variables. ie. Y=aX+b.  Mean and variance of Y. 
The cumulative distribution function for discrete and continuous random variables; calculating Normal probabilities (standardising), characteristic load and strength. 
Normal approximation to the Binomial distribution. Application to quality control. 

Coursework (week 9) Weighting within unit 20%

Examination (semester 1) Weighting within unit 80%

E. Kreysig, Advanced Engineering Mathematics, John Wiley

G James et. al., Modern Engineering Mathematics, Pearson

G James et. al., Advanced Modern Engineering Mathematics, Pearson

HELM (Helping Engineers Learn Mathematics) 

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard / course unit related emails for any further updates

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £37,500 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

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