2022/23 Undergraduate Module Catalogue
XJCV2560 Engineering Mathematics and Modelling 2
20 creditsClass Size: 200
Module manager: Dr. Duncan Borman
Email: d.j.borman@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2022/23
Pre-requisite qualifications
A-level Mathematics grade C or equivalent.Pre-requisites
| CIVE1560 | Engineering Mathematics and Modelling 1 |
Module replaces
Part of CIVE2602 and part of CIVE3599This module is not approved as a discovery module
Objectives
The module objectives are that students will:(i) develop an understanding of the principles of general basic mathematical techniques of relevance to Civil Engineers and develop sufficient mathematical competence to cope with the compulsory content of a Civil Engineering degree;
(ii) further develop appreciation of physical situations where the above mathematical techniques are useful;
(iii) be able to construct mathematical models from real problems, be able to model problems related to Civil Engineering and develop experience at using computational tools to solve engineering problems;
(iv) develop confidence in their mathematical abilities so that when this mathematics arises in the solution of an engineering problem they are able to understand (rather than merely accept) the results.
Learning outcomes
On completion of this module students students will be able to:
1. develop knowledge and understanding of mathematical principles to underpin their engineering education and understanding of the principles of general basic mathematical techniques relevant to Civil Engineers;
2. apply mathematical methods, tools and notations proficiently in the analysis and solution of engineering problems with an ability to apply quantiative methods and computational tools to relevant problems in engineering;
3. appreciate physical situations where mathematical techniques are useful and develop knowledge and understanding of mathematical models and their limitations;
4. have the ability to apply mathematical and computer-based models for solving engineering problems with appreciation of the model assumptions and their limitations;
5. develop models for problems related to Civil Engineering and gain experience using computational tools to solve engineering problems;
6. have confidence in their mathematical abilities so that when this mathematics arises in the solution of an engineering problem they are able to understand (rather than merely accept) the results.
(ii) apply mathematical methods, tools and notations proficiently in the analysis and solution of engineering problems with an ability to apply quantiative methods and computational tools to relevant problems in engineering;
(iii) appreciate physical situations where mathematical techniques are useful and develop knowledge and understanding of mathematical models and their limitations;
(iv) have the ability to apply mathematical and computer-based models for solving engineering problems with appreciation of the model assumptions and their limitations;
(v) be able to develop models for problems related to Civil Engineering and gain experience using computational tools to solve engineering problems;
(vi) have confidence in their mathematical abilities so that when this mathematics arises in the solution of an engineering problem they are able to understand (rather than merely accept) the results.
Skills outcomes
Team working
Syllabus
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, introduction and simple example of Fourier series.
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
- Modelling heat transfer (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.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| On-line Learning | 12 | 1.00 | 12.00 |
| Class tests, exams and assessment | 3 | 6.00 | 18.00 |
| Group learning | 2 | 2.50 | 5.00 |
| Lecture | 38 | 1.00 | 38.00 |
| Tutorial | 12 | 1.00 | 12.00 |
| Independent online learning hours | 35.00 | ||
| Private study hours | 80.00 | ||
| Total Contact hours | 85.00 | ||
| Total hours (100hr per 10 credits) | 200.00 | ||
Private study
Review of lecture materials;Directed prepartory work for modelling workshop;
Undertaking example sheets and background reading;
Undertaking formative and summative problem activities.
Opportunities for Formative Feedback
- Weekly/fortnightly Mathlab tasks;- Formative and summative Problem activities;
- Regular example classes;
- In class interaction and direct feedback (e.g. questions, clickers, ABCD cards, show of hands
Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| Project | Statistics coursework | 15.00 |
| Project | Extended project on modelling with differential equations | 10.00 |
| Problem Sheet | 2 Problem Sheets | 10.00 |
| Total percentage (Assessment Coursework) | 35.00 | |
Resit - 85% online time-limited assessment.; 15% Statistics assignment
Exams
| Exam type | Exam duration | % of formal assessment |
| Online Time-Limited assessment | 5 hr | 65.00 |
| Total percentage (Assessment Exams) | 65.00 | |
Resit - 85% online time-limited assessment.; 15% Statistics assignment
Reading list
The reading list is available from the Library websiteLast updated: 12/10/2022 14:44:32
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