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2021/22 Undergraduate Module Catalogue

CIVE2560 Engineering Mathematics and Modelling 2

20 creditsClass Size: 175

Module manager: Dr. Duncan Borman
Email: d.j.borman@leeds.ac.uk

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2021/22

Pre-requisite qualifications

A-level Mathematics grade C or equivalent.

Pre-requisites

CIVE1560Engineering Mathematics and Modelling 1

Module replaces

Part of CIVE2602 and part of CIVE3599

This 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.

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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Delivery typeNumberLength hoursStudent hours
On-line Learning121.0012.00
Class tests, exams and assessment36.0018.00
Group learning13.003.00
Lecture381.0038.00
Tutorial101.0010.00
Independent online learning hours35.00
Private study hours84.00
Total Contact hours81.00
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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information


Coursework
Assessment typeNotes% of formal assessment
ProjectStatistics coursework15.00
ProjectExtended project on modelling with differential equations10.00
Problem Sheet2 Problem Sheets10.00
Total percentage (Assessment Coursework)35.00

Resit - 85% online time-limited assessment; 15% Statistics assignment


Exams
Exam typeExam duration% of formal assessment
Online Time-Limited assessment3 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 website

Last updated: 30/06/2021 16:19:55

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