Engineering and design
Engineering Mathematics 2
Module code: H1042
Level 5
15 credits in autumn semester
Teaching method: Lecture, Workshop
Assessment modes: Unseen examination, Coursework
The Engineering Mathematics 2 module is divided into two sections.
The first builds on the mathematics you studied in the first year as you further study the solution of linear differential equations of various types – a topic of considerable importance in engineering analysis. You’ll also look at 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. Additionally you’ll consider basic methods for numerically solving first order ordinary differential equations. You’ll also explore solution methods for some of the partial differential equations common in engineering analysis, such as the heat and wave equations.
The second section of the module introduces you to 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.
Topics include:
- 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.
Pre-requisite
Engineering Maths 1A
Engineering Maths 1B
Programming for Engineers
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.