2022/23 Undergraduate Module Catalogue

XJCV1560 Engineering Mathematics and Modelling 1

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.

Module replaces

CIVE1620 and part of CIVE2602

This module is not approved as a discovery module

Module summary

n/a

Objectives

The module objective is 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) develop appreciation of physical situations where the above mathematical techniques are useful;

(iii) develop an understanding of what is meant by a mathematical model and be able to construct simple 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 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 quantitative methods and computational tools (e.g. Matlab, Excel) to relevant problems in engineering;

3. appreciate physical situations where these mathematical techniques are useful and develop knowledge and understanding of mathematical models and an appreciation of their assumptions and limitations;

4. construct simple mathematical models from real problems and have the ability to assess model limitations;

5. model problems related to Civil Engineering and develop experience at 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

- Numbers, functions and essential results from calculus: Functions; Differentiation: definition, first derivatives, second derivatives, techniques, maxima and minima; Curvature and radius of curvature; Methods of integration: definitions, basic functions, parts, substitutions, trigonometric functions, partial fractions; Numerical integration: the trapezium rule, Simpson's rule; Volumes and centroids (planes and volumes).
- Linear Equations: Solution of systems of linear equations by echelon method; linear equations arising from spring systems. Matrix Algebra: Operations with matrices; basic definitions; addition, scalar multiplication and matrix multiplication; Determinants; definition; rules for determinants; determinant calculation by application of the rules for determinants; Inverse of a matrix; definition; calculation by elementary operations; Linear equations (as matrices); applications of the inverse matrix; Eigenvalues and eigenvectors; calculation of eigenvalues and eigenvectors; illustration of an engineering application.
- Vector Algebra: General introduction; scalars and vectors; direction cosines; modulus of a vector; unit vectors; Addition of vectors; parallelogram and polygon rule; basic rules; Scalar products; definition in component and geometrical form; basic rules; angle between two vectors; perpendicularity of vectors; work done by a force; force components; Vector products; definition in component and geometrical form; basic rules; moment of forces; areas of triangles and parallelograms; parallel vectors; Vector treatment of lines; representations in vector and Cartesian form; intersection of lines.
- Numerical methods: Numerically defined functions -solution techniques, difference formulae, interpolation functions. Numerical differentiation- Euler's method, Higher order and Runge-Kutter methods.
- Ordinary differentiation Equations (ODE’s): General introduction, physical interpretation, 1st order ODE, solving using integration, simple approaches for solving numerically, engineering applications examples.
- Modelling: general, setting up a model, validation, modelling cycle, introduction to computation tools (Excel, Matlab e.g. for solving equations, matrix operations, graphing, setting up a basic mathematical model etc.)
- Complex numbers: definition, Argand Diagram, polar form, De Moivre's Theorem, finding complex roots of polynomial equations, setting up a basic mathematical model etc.)

The majority of students to:
(from Numbers, function & calculus)
- be able to understand and ascertain the behaviour of a range of simple and complex functions
- be able to differentiate a wide range of functions using range of appropriate methods
- be able to apply differentiation and algebraic manipulation appropriate for applying to core subjects in civil engineering
- be able to integrate a wide range of functions using appropriate methods
- understand how differentiation and integration can be used in applications relevant to engineering
- be able to solve simple ordinary differential equations and appreciate importance of differential equations for describing physical processes and their importance in engineering.
(From modelling workshop)
- understand what is meant by a mathematical model and be able to construct simple mathematical models from real problems
- use computational tools to solve engineering problems
- work successfully as a group
(From Matrices)
-be able to apply matrix methods and operations and apply to engineering problems
-be able to solve simple systems of equations using variety of approaches
(From vectors)
-understand vectors and be able to apply vector algebra to problems
(From numerical methods)
-understand what is meant by numerically defined functions and apply numerical difference formulae
-recognize the limitations and accuracies of numerical solution techniques.
(From complex numbers)
- be able to manipulate complex numbers in Cartesian and polar form, interpret them

Teaching methods

Delivery type	Number	Length hours	Student hours
On-line Learning	16	1.00	16.00
Class tests, exams and assessment	3	5.00	15.00
Group learning	4	2.50	10.00
Lecture	38	1.00	38.00
Tutorial	8	1.00	8.00
Independent online learning hours			35.00
Private study hours			78.00
Total Contact hours			87.00
Total hours (100hr per 10 credits)			200.00

Private study

Review of lecture materials.
Directed preparatory 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 examples 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
Report	Extended modelling coursework	10.00
Problem Sheet	3 Problem Sheet	15.00
Total percentage (Assessment Coursework)		25.00

Resit 100% online time-limited assessment.

Exams

Exam type	Exam duration	% of formal assessment
Online Time-Limited assessment	5 hr 00 mins	75.00
Total percentage (Assessment Exams)		75.00

The resit taken as external (inc. summer) will be 100% exam.

Reading list

The reading list is available from the Library website

Last updated: 12/10/2022 14:44:31

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