2023/24 Undergraduate Module Catalogue
XJME1520 Engineering Mathematics
20 creditsClass Size: 100
Module manager: Dr Mark Wilson
Email: M.Wilson@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2023/24
This module is not approved as a discovery module
Objectives
- To equip students with the knowledge and understanding of mathematical concepts, notation and techniques relevant to mechanical engineering.- To develop skills and confidence in mathematical modelling and problem solving.
- To support students in understanding mathematical aspects of other modules.
Learning outcomes
On successful completion of this module, students should be able to:
1. Use vectors to represent three-dimensional space, including points, lines and planes and find intersections among these.
2. Differentiate and integrate vectors in the context of dynamics problems, and understand scalar and vector products and their use in mechanics and dynamics.
3. Integrate and differentiate functions using a range of techniques and relate derivatives and integrals to engineering applications such as rates of change, maxima and minima, areas, volumes, averages, flow rates, work, centres of mass, etc.
4. Sketch (freehand) basic and composite functions, recognising limiting behaviours and discontinuities.
5. Create mathematical models of engineering systems described by first order ordinary differential equations, and solve the equations analytically and via Euler’s method.
6. Differentiate and integrate functions of more than one variable.
7. Understand the formation of matrices, their associated algebra, their use in the solution of simultaneous equations and in graphical transformations, and the concepts of eigenvalues and eigenvectors.
8. Understand, manipulate and plot complex numbers and functions in various forms, find complex solutions of equations, and appreciate the links between exponential, trigonometric and hyperbolic functions.
9. Present data effectively using a variety of techniques.
10. Calculate important statistical measures of central tendency and dispersion.
11. Understand the concept of correlation and regression, calculate the regression coefficient and determine regression lines via the least squares technique.
12. Understand the basic concepts of probability, including conditional probability and independence.
Upon successful completion of this module the following UK-SPEC learning outcome descriptors are satisfied:
Skills outcomes
Mathematical modelling and problem solving skills
Ability to apply mathematics to represent, analyse and design engineering systems.
Syllabus
Definitions and use of vectors in 3D space; vector algebra; the scalar and vector products and their uses.
Functions and graphs; limits of functions.
Techniques for differentiation: product rule; quotient rule; chain rule; implicit differentiation; logarithmic differentiation; differentiating parametric equations; differentiating vectors in Cartesian and polar coordinate systems.
Techniques for integration: substitution; integration by parts; partial fractions; integration of vectors; numerical integration.
Engineering applications of integration and differentiation.
Functions of more than one variable: partial differentiation; multiple integrals.
First order differential equations; mathematical modelling and problem solving.
Vector equations of lines and planes.
Matrix algebra; transformation matrices; eigenvalues and eigenvectors.
Complex numbers; hyperbolic functions.
Statistics, regression and elementary probability.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Class tests, exams and assessment | 1 | 2.00 | 2.00 |
| Class tests, exams and assessment | 2 | 1.00 | 2.00 |
| Lecture | 44 | 1.00 | 44.00 |
| Practical | 20 | 1.00 | 20.00 |
| Tutorial | 4 | 1.00 | 4.00 |
| Private study hours | 128.00 | ||
| Total Contact hours | 72.00 | ||
| Total hours (100hr per 10 credits) | 200.00 | ||
Private study
Reviewing lecture notes, solving example sheets, preparing for tutorials and class tests. Revising for final exam. Students are to spend 1 hour preparation for each lecture; 2 hours preparation for each tutorial; 10 hours preparation for each class test; a further 56 hours for exam preparation.Opportunities for Formative Feedback
Students will receive formative feedback from a class test in each semester.Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| In-course Assessment | Class test in semester 2 | 20.00 |
| In-course Assessment | Class test in semester 1 | 20.00 |
| Total percentage (Assessment Coursework) | 40.00 | |
Coursework marks carried forward and 60% resit exam OR 100% resit exam
Exams
| Exam type | Exam duration | % of formal assessment |
| Unseen exam | 2 hr | 60.00 |
| Total percentage (Assessment Exams) | 60.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 24/05/2023
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
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