# 2023/24 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** 2023/24

### 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 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

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 | 1 | 3.00 | 3.00 |

Lecture | 38 | 1.00 | 38.00 |

Tutorial | 10 | 1.00 | 10.00 |

Independent online learning hours | 35.00 | ||

Private study hours | 84.00 | ||

Total Contact hours | 81.00 | ||

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: 28/04/2023 14:52:55

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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