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Module details for 2024/25.

15 credits

FHEQ Level 4

Module Outline

Module Outline
The Engineering Maths 1B module follows on from the Engineering Maths 1A module, developing
the mathematical techniques studied in the context of their application to physical processes. In
the physical world many quantities change over space and these quantities may have diffferent
physical characteristics. For instance, the amount of electric charge in a region of space is a
scalar quantity, but the velocity of the flow of a liquid is described by a vector and hence is a vector
quantity. This module develops some of the mathematical tools needed to describe the changes
of these quantities with different characters (scalar or vector) in space. Many of these methods
will be useful in your later courses, for example, in electromagnetism and quantum mechanics.

Module Topics
Integration of vectors; point masses, coordinates of centres of mass of uniform lamina, moments
of mass, moments of inertia; sequences and series, infinite series, binomial series, power series,
Maclaurin and Taylor series; modelling with differential equations, solutions to first order differential
equations using separation of variables and integrating factor methods, solutions to second
order ordinary differential equations with constant coefficients; general solutions and unique solutions;
matrices: characteristic equations, eigenvalues and eigenvectors; multiple integration:
surface integrals, integration over non-rectangular regions, volume integrals, polar, cylindrical and
spherical co-ordinates; introduction to differential vector calculus: divergence, gradient or curl of
a vector or scalar field; line integrals, surface and volume integrals over scalar and vector fields;
Gauss and Stokes’ Theorems

Module learning outcomes

Be able to apply differential and integral multivariate calculus to the evaluation of line, surface and volume integrals and have an appreciation of the applications in engineering analysis.

Understand how to calculate power series expansions and have an appreciation of the applications in engineering analysis.

Be familiar with matrix algebra, including the calculation of Eigenvalues and Eigenvectors, and have an appreciation of their applications in engineering analysis.

Understand a variety of methods used to solve first and second order ordinary differential equations and have an appreciation of their applications in engineering analysis.

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.

Prof Jing Xu

Assess convenor
/profiles/544290