Engineering Mathematics IV
Module code: MAU22E02 · Semester: 2
Resources
Questions by Year
- 2025/26
- 2024/25
- 2023/24
- 2022/23
- 2021/22: MAU22E02_exam2022 · Paper 1
- 2019/20
- 2018/19 (old code MA2E02)
- 2017/18 (old code MA2E02)
- 2016/17 (old code MA2E02)
- 2015/16 (old code MA2E02)
- 2014/15 (old code MA2E02)
- 2013/14 (old code MA2E02)
- 2012/13 (old code MA2E02)
Topics
- Vector-valued functions: arc length, tangent, normal and binormal vectors LO2
- Partial derivatives, chain rule, gradients, directional derivatives, tangent planes LO1–2
- Maxima and minima of functions of two variables LO3
- Double and triple integrals, polar/cylindrical/spherical coordinates, Jacobians, centre of gravity LO4
- Vector fields, line integrals, conservative fields LO5
- Green's theorem, surface integrals, flux, divergence theorem, Stokes' theorem LO6
- Laplace transforms: shifting theorems, Heaviside and Dirac delta, convolution, ODEs LO7
Learning outcomes
- Analyse functions of several variables and find partial derivatives, including implicit ones
- Find tangent lines to curves and tangent planes to surfaces
- Find local and global extrema of functions of several variables
- Evaluate multiple integrals in Cartesian, polar, cylindrical and spherical coordinates for areas, volumes, masses and centroids
- Test whether a field is conservative, find its potential and evaluate line integrals
- Use Green's, Stokes' and the divergence theorems
- Solve differential equations with Laplace transforms