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Semester 2

Engineering Mathematics 2B (SCEE08010)

Subject

Engineering

College

SCE

Credits

10

Normal Year Taken

2

Delivery Session Year

2023/2024

Pre-requisites

Mathematics units passed equivalent to Mathematics for Science and Engineering 1a and Mathematics for Science and Engineering 1b.

Course 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 integrationLecture 1: Scalar and vector fields, the gradientLecture 2: Conservative fields, divergence and curlLecture 3: Harmonic fields, vector calculus lawsLecture 4: Line integration, the work integralLecture 5: Flux integrals, scalar line integralsLecture 6: Work and flux integrals in polar coordinatesLecture 7: Double integration, changing the orderLecture 8: Variable transformations and double integrals in polarLecture 9: Green's theorems for work and fluxLecture 10: Triple integrals, cylindrical coordinatesTheme 2: Applied probability and statisticsLecture 11: Probability axioms, laws and Venn diagramsLecture 12: Independence, conditional probability, Bayes theorem, discrete random variablesLecture 13: Continuous random variables, random variable transformationsLecture 14: Joint random variables, conditional distribution, convolutionLecture 15: Law of large numbers, central limit theorem, sums of random variablesLecture 16: Maximum likelihood estimator, bias, efficiency and mean squared errorLecture 17: Confidence intervals, non-rejection regionsLecture 18: Hypothesis testing, type I & II errors, power of the test, p valueLecture 19: Critical values and quantiles, Z and T hypothesis tests, Gaussian approximation of the binomialLecture 20: Linear regression, least squaresBoth 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.

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

Additional Assessment Information

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.

view the timetable and further details for this course