Program Overview

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Module Overview

A first-level engineering mathematics module designed to briefly revise and then extend A-Level maths material and introduce more mathematical techniques to support engineering science modules.

Module Provider

Sustainability, Civil & Env Engineering

Module Leader

ASTON Philip (Physics)

Number of Credits

15

ECTS Credits

7.5

Framework

FHEQ Level 4

Module Cap (Maximum number of students)

N/A

Overall Student Workload

• Independent Learning Hours: 84
• Tutorial Hours: 11
• Guided Learning: 33
• Captured Content: 22

Module Availability

Semester 1

Prerequisites / Co-requisites

Normal entry requirements for the degree programmes in Civil Engineering or Chemical and Process Engineering.

Module Content

Indicative content includes:

• Functions: Briefly revise the concept of a function; domain, range. Odd, even and periodic functions. Trig functions. Hyperbolic functions. Exponential and logarithmic functions and their graphs. Inverse functions. Algorithms. Numerical methods. Series and limits. Examples with engineering context.
• Differentiation: Briefly revise the concept of derivative and rules of differentiation for a function of one variable. Applications to gradients, tangents and normals, extreme points and curve sketching, Taylor and Maclaurin series. Formulating differential equations. Functions of several variables: partial derivatives for functions of several variables, total derivative, application to small changes in a function and errors. Extrema of functions of two variables. Examples with engineering context.
• Integration: Briefly revise the concept of indefinite integration as the inverse of differentiation and standard methods for integration such as substitution, integration by parts and integration of rational functions. Definite integration, area under curves, use of recurrence relationships. Applications of integration to curve lengths, surfaces and volumes of revolution, first moments and centroids, second moments and radii of gyration. Simple double integrals.
• Probability and Statistics: Descriptive statistics: numerical (mean, mode, median, variance etc) and graphical summaries. Basic probability: elementary laws, random variables, mean and variance. Discrete probability distributions (binomial, Poisson); continuous probability distributions (normal). Statistics with Matlab.
• Mechanics: Vectors as quantities with magnitude and direction, graphical representation, addition and subtraction, unit vectors, scalar (dot) product, projection, resolution into components; cross (vector) product. SUVAT equations.
• Complex numbers: Real and imaginary parts, polar form, Argand diagram, exp(jx), De Moivre's theorem and applications.

Assessment Pattern

Assessment type	Unit of assessment	Weighting
Online Scheduled Summative Class Test	ONLINE IN SEMESTER TEST (50 MINS)	30
Examination Online	ONLINE 24 HOUR (OPEN BOOK) EXAM	70

Alternative Assessment

None

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their knowledge of mathematical concepts and rules, and to show their skills in solving mathematical and engineering problems using appropriately selected techniques.

Module Aims

• Consolidate and extend students' knowledge of basic mathematical concepts and techniques relevant to the solution of engineering problems
• Make students aware of possible pitfalls
• Enable students to select appropriate methods of solution
• Enable students to apply their mathematical knowledge and skills to engineering problems

Learning Outcomes

Ref	Attributes Developed
001	Manipulation of standard functions	KCPT	SM2B
002	Use of the techniques of differential and integral calculus for functions of one and two variables	KCPT	SM2B
003	Application of differentiation and integration to determine physical engineering properties	KCPT	SM2B
004	Calculation of probabilities and summary statistics.	KCPT	SM2B
005	Use of vector algebra and applications of this to mechanics	KCPT	SM2B
006	Use of complex numbers	KCPT	SM2B

Attributes Developed

• C - Cognitive/analytical
• K - Subject knowledge
• T - Transferable skills
• P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to familiarise students with mathematical concepts and techniques, supported by extensive use of examples and applications; students themselves are engaged in the solution of problems and application of techniques in tutorials/problems classes.

• Lectures (4 hrs/wk for 10 weeks, 2 hrs/wk for 1 week) to revise underpinning prior learning and bring students from varying background to a common level of knowledge, and to introduce new concepts and techniques and provide illustrative examples and applications.
• Labs (2 hrs/wk for 1 week) to introduce Matlab as a tool for performing calculations in Statistics.
• Recommended wider reading of matching sections of relevant recommended texts.
• Problem sheets of examples for technique selection and skill development.
• Tutorials/problems classes (1 hr/wk for 11 weeks) with staff and PG assistance for the development of skills in technique application and also in selection of appropriate techniques, using the above problems sheets; assistance is given both at individual level, and for the group on common areas of difficulty
• Coursework (summative but also formative) to assess technique selection and skill development
• Examination

Programmes this Module Appears In

Programme	Semester	Classification	Qualifying conditions
Chemical and Petroleum Engineering BEng (Hons)	1	Compulsory	A weighted aggregate mark of 40% is required to pass the module
Chemical and Petroleum Engineering MEng	1	Compulsory	A weighted aggregate mark of 40% is required to pass the module
Chemical Engineering BEng (Hons)	1	Compulsory	A weighted aggregate mark of 40% is required to pass the module
Chemical Engineering MEng	1	Compulsory	A weighted aggregate mark of 40% is required to pass the module
Civil Engineering BEng (Hons)	1	Compulsory	A weighted aggregate mark of 40% is required to pass the module
Civil Engineering MEng	1	Compulsory	A weighted aggregate mark of 40% is required to pass the module