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
|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.
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.
Information for Visiting Students
|Pre-requisites||Mathematics units passed equivalent to Mathematics for Science and Engineering 1a and Mathematics for Science and Engineering 1b.
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
||Students must pass BOTH the Exam and the Coursework.
The School has a 40% Rule for 1st and 2nd year courses, i.e. you must achieve a minimum of 40% in coursework and 40% in written exam components, as well as an overall mark of 40% to pass a course. If you fail a course you will be required to resit it. You are only required to resit components which have been failed.
||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 fields
- Ability 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
|Keywords||Vector calculus,Multiple integrals,Statistical method,Regression,Probability
|Course organiser||Dr Nicholas Polydorides
Tel: (0131 6)50 2769
|Course secretary||Miss Mhairi Sime
Tel: (0131 6)50 5687