 # DEGREE REGULATIONS & PROGRAMMES OF STUDY 2021/2022

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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 The course consists of two main themes: Theme 1: Vector calculus and integration of in two parts, taught in the first half of the term in weeks 1-5, and Theme 2: Introduction to probability and statistics, at the second half in weeks 6-10. In the first 10 lectures on theme 1 I will introduce the concepts of scalar and vector fields in 2 and 3 dimensions and give real-world examples of such fields in engineering systems. We will cover differentiation of these fields as well as line, double, triple and surface integration focusing on work and flux integrals. For the second theme we also have a total of 10 lectures, where 2D integration of scalar fields is fundamental, we will introduce the concepts of random events and variables, as well as the axioms of probability, with emphasis on the conditional probabilities, independence, Bayes¿ theorem, the law of large numbers and the central limit theorem. In the second half of theme 2, we switch from probability to statistics to learn about point estimators from data, their bias and variance, and then interval estimators and how to conduct hypothesis tests using data samples, explain how to compute the p-value and the power of the tests, before we close with an introduction in linear regression and the least squares method which is ubiquitous in engineering analysis. The course has 2 handwritten coursework assessments with 10% of the credit each, one on each theme, and a final exam on both themes for the remaining 80% of the credit. Each coursework is scheduled for a 10 hour load including preparation reading. There will also be 4 online quizzes, two on each theme that the students are encouraged to do for formative feedback and self-assessment. In every aspect of the delivery and assessment, i.e. lectures, tutorials, coursework, exam questions, themes 1 and 2 carry equal merit. Course description Theme 1: Vector calculus and integration Lecture 1: Scalar and vector fields, the gradient Lecture 2: Conservative fields, divergence and curl Lecture 3: Harmonic fields, vector calculus laws Lecture 4: Line integration, the work integral Lecture 5: Flux integrals, scalar line integrals Lecture 6: Work and flux integrals in polar coordinates Lecture 7: Double integration, changing the order Lecture 8: Variable transformations and double integrals in polar Lecture 9: Green's theorems for work and flux Lecture 10: Triple integrals, cylindrical coordinates Theme 2: Applied probability and statistics Lecture 11: Probability axioms, laws and Venn diagrams Lecture 12: Independence, conditional probability, Bayes¿ theorem, discrete random variables Lecture 13: Continuous random variables, random variable transformations Lecture 14: Joint random variables, conditional distribution, convolution Lecture 15: Law of large numbers, central limit theorem, sums of random variables Lecture 16: Maximum likelihood estimator, bias, efficiency and mean squared error Lecture 17: Confidence intervals, non-rejection regions Lecture 18: Hypothesis testing, type I & II errors, power of the test, p value Lecture 19: Critical values and quantiles, Z and T hypothesis tests, Gaussian approximation of the binomial Lecture 20: Linear regression, least squares Both themes are supported by tutorial classes every week from week 2 to 11. For theme 2, students will require to become familiar in using the R statistical software, and they will be assessed on it. Lecture slides and instructor notes which also include solved examples and narrated exercises as well as self-assessment questions and answers will be provided for every lecture's material. Unless specified explicitly in the lectures, all material presented in lecture slides and exercises is examinable.
 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 advised to consult Advanced Modern Engineering Mathematics by Glyn James, Prentice Hall, ISBN 978-0-273-71923-6 (any edition)
 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 2021/22, 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) Students must pass BOTH the Exam and the Coursework. Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) 1:30 Resit Exam Diet (August) 1:30
 On completion of this course, the student will be able to: Understanding of scalar and vector fields, differential operators for gradient, divergence and curl, line integrals for work and flux, Green's theorems on the plane and their implications on conservative and solenoidal fieldsAbility to use the basic vector differential identities and to calculate integrals over simple 2D and 3D geometries.Understanding the concepts of random events and variables, common discrete and continuous probability distributions, joint and independent random variables.Ability to compute point and interval estimators from data and quantify their error,Ability to perform statistical hypotheses tests and linear regression analysis
 Students are expected to access 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 Additional reading list 1. Michael Corral, Vector Calculus (electronic copy free to use from the library) 1. Blitzstein, Joseph K ; Hwang, Jessica, Introduction to Probability (electronic copy free to use from the library. Covers the material of the first half of theme 2) 2. Sarah Stowell. Using R for Statistics. Apress, 2014. ISBN 978-1-484-20140-4. 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,Statistical method,Regression,Probability
 Course organiser Dr Nicholas Polydorides Tel: (0131 6)50 2769 Email: N.Polydorides@ed.ac.uk Course secretary Miss Jennifer Yuille Tel: (0131 6)51 7073 Email: Jennifer.Yuille@ed.ac.uk
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