# Engineering Maths 1B (H1034)

15 credits, Level 4

Spring teaching

This is the second of two mathematics modules taken in the first year. You will continue to build on A-level topics relevant to engineers.

In the physical world many quantities change over space and time. You‘ll examine their characteristics as scalar or vector quantities, and develop the mathematical tools needed to describe these changes. This will build to the application of vector calculus to problems in one, two and three dimensions, in both scalar and force fields.

You will continue to develop the tools necessary for later years’ modules. You are encouraged to offer feedback in lectures, and will be exposed to many worked and guided examples and questions for practice.

Topics include:

• integration of vectors; co-ordinates of centres of mass, moments of inertia
• sequences and series: summation notation, arithmetic and geometric series; convergence to a limit, absolute and conditional convergence, tests for convergence
• binomial series, the Binomial Theorem, general power series, Maclaurin and Taylor series expansions and error estimations
• classification of differential equations
• solution of first order ordinary differential equations using separable variable and integrating factor methods
• solution of second order ordinary differential equations with constant coefficients (homogeneous and non-homogenous)
• matrices: calculation of eigenvalues and eigenvectors; linear independence of eigenvectors; basic properties
• double integrals as surface integrals over rectangular and non-rectangular regions
• volume integrals using cartesian, cylindrical and spherical co-ordinates
• scalar field and vector fields
• gradient of a scalar field; divergence of curl of a vector field
• scalar and vector line integrals
• surface and volume integrals in a vector field
• the use of Gauss and Stokes’ Theorems to facilitate vector integration.

### Teaching

79%: Lecture
21%: Practical (Workshop)

### Assessment

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