# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2016/2017

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# Undergraduate Course: Engineering Mathematics 2B (SCEE08010)

 School School of Engineering College College of Science and Engineering Credit level (Normal year taken) SCQF Level 8 (Year 2 Undergraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 Summary This course is in two parts, taught simultaneous with one lecture per week. The first part, mathematical methods, covers: Multivariate integration and vector calculus for engineering. Gradient, tangent plane, normals; Scalar and vector fields; divergence and curl; conservative fields and potential; vector differential identities; simple applications from properties of continua and electromagnetism. Repeated multiple integration (change of order of integration); integration in non-cartesian coordinates, Jacobian; line integrals (link to potential and work); surface integrals (flux); divergence, Green's and Stokes' theorems; applications and physical interpretations; The second part, quantitative methods, covers: descriptive statistics and the presentation of statistical data; probability theory; discrete and continuous probability density functions; hypothesis testing (including 1-way ANOVA); regression and experimental design. Course description Mathematical Methods: - Vector Calculus: * Basic concepts, Transformations [1 lecture] * Gradient [0.5 lecture] * Divergence and curl [1.5 lectures] - Integration: * Double Integrals [3 lectures] * Line integrals [1.5 lectures] * Green's Theorem [0.5 lecture] * Surface Integrals [2 lectures] * Volume Integrals [1 lecture] * Gauss' Theorem [0.5 lecture] * Stokes' Theorem [0.5 lecture] Quantitative Methods: - Descriptive Statistics [1 lecture] - Graphical presentation of data [1 lecture] - Probability theory [1 lecture] - Discrete distributions [1 lecture] - Continuous distributions [1 lecture] - Hypothesis testing: t-test [ 1 lecture] - Hypothesis testing: power of the test, 1 way ANOVA [1 lecture] - Linear Regression including tests for regression line [1 lecture] - Non-linear and multivariate regression [1 lecture] - Experimental design [1 lecture] The mathematical methods material will be supported by tutorial classes every other week. These will alternate with quantitative methods laboratory classes using the R statistical software.
 Pre-requisites It is RECOMMENDED that students have passed Mathematics for Science and Engineering 1a (MATH08060) AND Mathematics for Science and Engineering 1b (MATH08061) Co-requisites Prohibited Combinations Other requirements None Additional Costs Students are expected to own a copy of Advanced Modern Engineering Mathematics by Glyn James, Prentice Hall, ISBN 978-0-273-71923-6
 Pre-requisites Mathematics units passed equivalent to Mathematics for Science and Engineering 1a and Mathematics for Science and Engineering 1b. High Demand Course? Yes
 Academic year 2016/17, Available to all students (SV1) Quota:  None Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 20, Seminar/Tutorial Hours 5, Supervised Practical/Workshop/Studio Hours 5, Formative Assessment Hours 2, Summative Assessment Hours 10, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 56 ) Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % Additional Information (Assessment) Written Exam 80%: Coursework 20%: Students must pass both the Exam and the Coursework. The Mathematical methods coursework comprises 5 pieces of work of which a minimum of 4 must be submitted. One piece of quantitative methods coursework will be set which must also be submitted. Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) Engineering Mathematics 2B 1:30 Resit Exam Diet (August) Engineering Mathematics 2B 1:30
 1. An understanding of vector fields, their divergence and curl. 2. An ability to use the basic vector differential identities. 3. A competence in evaluating repeated and multiple integrals. 4. An understanding of line integrals, their calculation and relation to the potential of a conservative field. 5. An ability to calculate integrals, such as flux, over simple curved surfaces. 6. An ability to use the divergence theorem and Stokes's theorem in simple situations, and a realization of their great practical importance. 7. An understanding of the presentation of statistical data using graphical methods and descriptive statistics. 8. A knowledge of probability theory. 9. An understanding of common discrete and continuous probability distributions. 10. An ability to describe and test statistical hypotheses using appropriate tests. 11. An ability to both lines of best fit and log-laws using regression techniques, including the interpretation of the slope and intercept of the line. 12. An understanding of the use of replication and randomization to control error in experiments and the use of Analysis of Variance techniques to determine significant factors.
 Students are expected to own a copy of : 1. Advanced Modern Engineering Mathematics by Glyn James, Prentice Hall, ISBN 978-0-273-71923-6 Students are recommended to download a copy of the free, open source, R statistics package from www.r-project.org Reading list 1. Sarah Stowell. Using R for Statistics. Apress, 2014. ISBN 978-1-484-20140-4. 2. Brian Dennis. The R Student Companion. Chapman & Hall/CRC Press, 2012. ISBN 978-1-439-87540-7 3. William Navidi, Statistics for Engineers and Scientists, McGraw-Hill, 2014. ISBN 978-1-259-25160-3
 Graduate Attributes and Skills Not entered Keywords Vector calculus,Multiple integrals,Line integrals,Statistical method,Regression,Data presentation
 Course organiser Prof David Ingram Tel: (0131 6)51 9022 Email: David.Ingram@ed.ac.uk Course secretary Miss Lucy Davie Tel: (0131 6)51 7073 Email: Lucy.Davie@ed.ac.uk
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