Engineering Maths 1B (H1034)
Engineering Maths 1B
Module H1034
Module details for 2023/24.
15 credits
FHEQ Level 4
Pre-Requisite
Engineering Maths 1A
Module Outline
The Engineering Mathematics 1B module is the second of two mathematics modules taken in the first year. We continue to build on and extend A level topics of relevance to engineers. In the physical world many quantities change over space and time. We examine their characteristics as scalar or vector quantities, and develop the mathematical tools needed to describe these changes, culminating in the application of vector calculus to problems in one, two and three dimensions in both scalar and force fields. We continue to develop the tools that are necessary for use in later years’ modules. Students are encouraged to offer feedback in lectures to ensure that the pace and their comprehension is optimal. They are exposed to many worked and guided examples and questions for practice.
The syllabus addresses the AHEP4 Learning Outcomes: C1, M1; C2, M2; and C3, M3.
Module Topics
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.
Library
Helping Engineers Learn Mathematics (HELM); helm@lboro.ac.uk
Bostock and Chandler, Pure Mathematics Volume 2, Nelson Thornes Ltd
Kreysig, Advanced Engineering Mathematics, 9th edition, Wiley International
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.
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Semester 2 Assessment | 80.00% |
| Coursework | 20.00% | |
| Coursework components. Weighted as shown below. | ||
| Problem Set | T2 Week 10 | 50.00% |
| Problem Set | T2 Week 7 | 50.00% |
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.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Spring Semester | Workshop | 1 hour | 01111111110 |
| Spring Semester | Lecture | 1 hour | 33333333333 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Carole Becker
Assess convenor
/profiles/103997
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