Module manager: Dr. Duncan Borman
Email: d.j.borman@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2025/26
This module is not approved as a discovery module
This module further develops fundamentals and application of mathematical knowledge and skills that civil and architectural engineering students need to succeed in their courses and for their future professional career. It includes limits and series, partial differentiation, differential equations, numerical methods/approaches, statistics and the modelling of engineering problems. The module has a strong focus on the application of mathematics and is therefore articulated around practical problems in statics, dynamics, fluid mechanics, and computation.
The module has the following objectives:
- To build on students' prior mathematical knowledge and skills to provide them with a comprehensive understanding of the mathematical concepts and techniques of practical relevance to engineers and develop sufficient competence to use them in their studies.
- To develop a broad appreciation of the contexts and problems where these mathematical techniques can be useful.
- To develop experience of using and developing mathematical models and for students to be able to model engineering problems, and to select and successfully use mathematical and computational tools to solve them.
- To develop students’ confidence in their mathematical abilities so that the techniques used, and the results obtained in different situations can be understood rather than merely accepted.
On successful completion of the module, students will have demonstrated the following learning outcomes (contributing to the AHEP4 learning outcomes indicated between brackets):
1- Apply a profound knowledge and understanding of mathematics to the solution of complex problems in the context of architectural and civil engineering. (C1/M1)
2- Formulate appropriate mathematical models that can be used to analyse complex engineering problems to reach substantiated solutions, discussing the limitations of the models and techniques employed. (C2/M2)
3- Select and apply appropriate computational tools (e.g. MATLAB, Excel) in the analysis and solution to range of engineering problems (including complex problems). (C3/M3)
4- Use practical skills to utilise mathematical models to investigate engineering problems. (C12/M12)
5- Apply statistical analysis and approaches in the context of architectural and civil engineering. (C1/M1)
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a- Data analysis (presenting and interpreting data)
b- IT/computational (spreadsheets, computational tools)
c- Problem solving
d- Collaboration
e- Information, data and media literacies
f- Digital proficiency
FUNCTIONS OF MULTIPLE VARIABLES AND PARTIAL DIFFERENTATION
Functions of more than one independent variables; first partial derivatives; Chain rule for first partial derivatives; Second partial derivatives and chain rule; application of chain rule for change of variable, approximating small errors, classifying maxima/minima/saddle points, grad; engineering application.
LIMITS, SEQUENCES AND SERIES
Series: Taylor polynomials; Taylor's theorem; expansion of functions; Maclaurin's expansion of functions; use of known series to give expansion of more complex functions; Approximations.
Limits: Sequences; Series: the limit of a series; convergence/divergence; the ratio test for convergence; power series; The limit of a function
DIFFERENTIAL EQUATIONS
- ANALYTICAL METHODS ODE's (1st/2nd order)
1st Order Ordinary Differential Equations: separable, exact, linear, homogeneous, 2nd Order Ordinary Differential Equations: linear homogeneous equations with constant coefficients, Linear inhomogeneous equations, with exponential, sinusoidal, and polynomial right-hand sides.
- Simple mathematical modelling of engineering applications using differential equations.
- NUMERICAL METHODS FOR ODE's
Numerically defined functions: solution techniques, difference formulae, interpolation functions; Taylor's series and truncation error; Numerical differentiation: boundary value problems, initial value problems, Euler's method and higher order Runge-Kutter methods.
- NUMERICAL METHODS FOR PDE's
Partial differential equations: Laplace equation and its solution; difference formulae; solving time dependent problems with simple time marching schemes (e.g. 1D transient heat equation);
- DIFFERENTIAL EQUATIONS - MODELLING ENGINEERING APPLICATIONS
Application of numerical gradients, finite difference approach to:
- Modelling heat equation (steady-state and transient)
- Modelling dynamic systems (e.g. Mass-spring-damper)
- COMPUTATIONAL TOOLS
-Using Excel/Matlab to implement the above models of engineering problems (involving differential equations).
STATISTICS
Summary statistics (measures of central tendency spread (e.g. mean, mode, standard deviation, quartiles etc); Probability distributions: the basic rules of probability, the use and characteristics of the main probability distributions with illustrations (normal distribution, Poisson, binomial, t and f); Hypothesis testing: for examination of significant differences between samples of data and also between the samples and an apriority belief of its population characteristics (null and alternative hypothesis, 1-tailed and 2-tailed tests, test statistics, significance levels); basic regression modelling: basic principles of simple regression modelling including interpretation of diagnostic statistics.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Example Class | 5 | 1 | 5 |
| Lecture | 19 | 2 | 38 |
| Practical | 1 | 3 | 3 |
| Independent online learning hours | 64 | ||
| Private study hours | 90 | ||
| Total Contact hours | 46 | ||
| Total hours (100hr per 10 credits) | 200 | ||
- Weekly mobius tasks – that give automated feedback;
- Formative and summative Problem sheets;
- The Modelling Coursework has an initial 2-side formative submission that students get feedback on prior to final submission
- Regular example activities in weekly sessions;
- In class interaction and direct feedback (e.g. questions, ABCD cards/show of hands, groups feeding back on tasks)
The Mobius maths-based assessment tool on Minerva is used to provide weekly, short formative assessments/activity which have automated marking and feedback of maths-based questions linked to topics being delivered (the engagement with these is monitored and content/feedback discussed in weekly in person sessions).
The summative coursework, each includes useful formative feedback for the students that will help students be successful in the module (and final assessment).
Other formative feedback is used in the interactive lecture sessions and workshops (e.g. linked to pre-work). (e.g. using group work, vevox quizzes and similar).
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team