THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2021/2022

Information in the Degree Programme Tables may still be subject to change in response to Covid-19

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Undergraduate Course: Engineering Mathematics 2B (SCEE08010)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThe 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 4 online coursework assessments with 10% of the credit each, 2 on each theme., and a final exam on both themes for the remaining 60% of the credit. 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 week 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. All material presented, in lecture slides and exercises is examinable.
Entry Requirements (not applicable to Visiting Students)
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)
Information for Visiting Students
Pre-requisitesMathematics units passed equivalent to Mathematics for Science and Engineering 1a and Mathematics for Science and Engineering 1b.
High Demand Course? Yes
Course Delivery Information
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) Written Exam 60%:
Coursework 40%:

Students must pass BOTH the Exam and the Coursework.
There will be a total of 4 courseworks, all electronic via Learn, 2 per theme.
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
Learning Outcomes
On completion of this course, the student will be able to:
  1. 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 fields
  2. Ability to use the basic vector differential identities and to calculate integrals over simple 2D and 3D geometries.
  3. Understanding the concepts of random events and variables, common discrete and continuous probability distributions, joint and independent random variables.
  4. Ability to compute point and interval estimators from data and quantify their error,
  5. Ability to perform statistical hypotheses tests and linear regression analysis
Reading List
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

Additional Information
Graduate Attributes and Skills Not entered
KeywordsVector calculus,Multiple integrals,Statistical method,Regression,Probability
Contacts
Course organiserDr Nicholas Polydorides
Tel: (0131 6)50 2769
Email: N.Polydorides@ed.ac.uk
Course secretaryMiss Jennifer Yuille
Tel: (0131 6)51 7073
Email: Jennifer.Yuille@ed.ac.uk
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