2024/25 Undergraduate Module Catalogue

CIVE1560 Engineering Mathematics and Modelling 1

20 creditsClass Size: 200

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

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

Year running 2024/25

Pre-requisite qualifications

Admission to UG programmes in the School of Civil Engineering

This module is not approved as a discovery module

Module summary

This module covers the fundamentals 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: calculus, vector and matrix algebra, and an introduction to mathematical models, numerical methods, and differential equations. The module has a strong focus on the application of mathematics and is therefore articulated around practical problems in statics, fluid mechanics, and computation.

Objectives

The module has the following objectives:

-To provide students with an understanding of the mathematical concepts and techniques of practical relevance to engineers and develop sufficient competence to use them in their studies.
-To develop an appreciation of the contexts and problems where these mathematical techniques can be useful.
-To introduce students to what is meant by a mathematical model and for students to be able to define and formulate mathematical models representing problems of increasing complexity.
-To learn how to model engineering problems and how 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.

Learning outcomes
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 more 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 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 of engineering problems. (C3/M3)
4. Use practical skills to utilise mathematical models to investigate engineering problems. (C12/M12)


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

Syllabus

CALCULUS:
-Functions.
-Differentiation: definition, first derivatives, second derivatives, techniques, implicit differentiation, maxima and minima.
-Curvature and radius of curvature.
-Methods of integration: basic functions, parts, substitutions, trigonometric functions, partial fractions, double integrals.
-Numerical integration: the trapezium rule, Simpson's rule.
-Volumes and centroids (planes and volumes).

ORDINARY DIFFERENTIAL EQUATIONS (ODEs):
-General introduction, physical interpretation, first order ODEs, solving using integration, simple approaches for solving numerically, engineering applications examples.

MODELLING:
-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)

LINEAR ALGEBRA:
-Linear equations, solution of systems of linear equations, linear equations describing spring systems.
-Vectors: direction cosines, modulus, unit vectors, operations with vectors, angles, orthogonality, projection, scalar and vector products, components of a force, work done by a force, moments, areas, representations in vector and Cartesian form, intersection of lines.
-Matrices: operations with matrices, scalar multiplication and matrix multiplication, determinants, inverse of a matrix, linear equations (as matrices).
-Singular value decomposition of matrices: eigenvalues and eigenvectors, geometric interpretation and calculation, applications in engineering.

NUMERICAL METHODS:
-Numerically defined functions:solution techniques, difference formulae, interpolation functions.
-Root-finding approaches (e.g. Newton Raphson, bisector, false position).
-Numerical differentiation: Euler's method, Higher order and Runge-Kutter methods.

COMPLEX NUMBERS: definition, Argand Diagram, polar form, De Moivre's Theorem, finding complex roots of polynomial equations)

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of:

2 x Coursework
1 x In-person open-book exam (invigilated)

Teaching methods

Delivery type	Number	Length hours	Student hours
Lectures	19	2.00	38.00
Practicals	4	2.00	8.00
Independent online learning hours			50.00
Private study hours			104.00
Total Contact hours			46.00
Total hours (100hr per 10 credits)			200.00

Opportunities for Formative Feedback

The 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).

Reading list

There is no reading list for this module

Last updated: 10/06/2024

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