# MEng Mechanical Engineering with Industrial Experience

Year of entry: 2023

## Course unit details:Mathematics 2M1

Unit code MATH29661 10 Level 2 Semester 1 Department of Mathematics No

### Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematics 1M2 MATH19662 Pre-Requisite Compulsory

### Aims

The course unit aims to provide a second year course in mathematics and statistics to students in the School of MACE.

### Learning outcomes

Knowledge and understanding: Demonstrate knowledge of the mathematical topics in the syllabus and their relevance to Mechanical, Aerospace, and Civil, Engineering.

Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.

Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host department or in subsequent years.

### Syllabus

3 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. Note 3

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

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

4 lectures: 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.

8 lectures: 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.

### Assessment methods

Method Weight
Other 20%
Written exam 80%

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 MathematicsPearson

G James et. al., Advanced Modern Engineering MathematicsPearson

HELM (Helping Engineers Learn Mathematics)

### Study hours

Scheduled activity hours
Lectures 24
Tutorials 11
Independent study hours
Independent study 65

### Teaching staff

Staff member Role
Robert Gaunt Unit coordinator
Chris Johnson Unit coordinator