# Engineering Mathematics 2 (H1042)

15 credits, Level 5

Autumn teaching

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.

### Teaching

77%: Lecture
23%: Practical (Workshop)

### Assessment

20%: Coursework (Problem set)
80%: Examination (Unseen examination)