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Module details for 2022/23.

15 credits

FHEQ Level 5

Module Outline

The Engineering Mathematics 2 module is divided into two sections. The first builds on the mathematics studied in the first year Engineering Mathematics1A and 1B modules by the further study of the solution of linear differential equations of various types, a topic of considerable importance in engineering analysis. These methods are then extended to cover methods of transforming linear differential equations into the frequency domain using the Laplace transform, a method that is central to the analysis of modern engineering control systems. A brief section then considers some basic methods for numerically solving first order ordinary differential equations. Solution methods for some of the partial differential equations common in engineering analysis, such as the heat and wave equations, are then detailed. The second section of the module introduces probability theory and statistical methods, illustrated with examples showing how these concepts can be used to gain estimates of the outcomes of the complex interactions that often occur in real engineering systems.

Module Topics
Revision of first order and second order differential equation time domain solution methods. Laplace transform and associated theorems; convolution. Solution of ODEs via the Laplace transform. Numerical solution of first order ODEs. Partial differential equations; separation of variables; outline of Fourier series solution; Laplace, Poisson, heat and wave equations. Probability: random variables; Bayes’ theorem; continuous and discrete distribution and density functions; expectations; normal distribution; central limit theorem; estimation of parameters; moment and maximum likelihood methods; student’s t-test; confidence intervals; quality control; acceptance sampling; reliability; failure rates; the Weibull distribution.

The syllabus thus addresses the AHEP4 Learning Outcomes: C1, M1; C2, M2; and C3, M3.

Pre-Requisite

Engineering Maths 1A
Engineering Maths 1B
Programming for Engineers

Library

Kreyszig, E., 2011, Advanced Engineering Mathematics, 10th Edition, Wiley

Stroud, K.A. and Booth, D., 2013 Engineering Mathematics, 7th edition. Basingstoke: Palgrave Macmillan

Riley K. F., Hobson M. P. and Bence S. J., 2004, Mathematical Methods for Physics and Engineering CUP 2nd edition

Chatfield C., 1989. Statistics for Technology, Chapman & Hall, 3rd edition.

Mendenhall W. and Sincich T., 1995, Statistics for Engineering and the Sciences, Prentice Hall, 4th edition.

Devore J. L., 2004, Probability and Statistics for Engineering and the Sciences, Thomson, 6th edition.
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De Veaux R. D., Velleman P. F. and Bock D. E., 2005, Stats: Data and Models, Pearson.

Module learning outcomes

Understand the essential features and properties of ordinary differential equations;

Apply different solution methodologies to ordinary differential equations including classical linear theory, Laplace transforms, and numerical methods, in order to gain physical insight into solutions.

Apply solution methods to partial differential equations commonly encountered in engineering with examples of detailed solution methods for the heat and wave equations.

Understand the essentials of probability theory and statistics, and how inferences from sampled data can be quantified and used to make meaningful decisions.

View timetable

Timing

Submission deadlines may vary for different types of assignment/groups of students.

Weighting

Coursework components (if listed) total 100% of the overall coursework weighting value.

How to read the week pattern

The numbers indicate the weeks of the term and how many events take place each week.

Dr Rupert Young

Assess convenor
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