# 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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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Several Variable Calculus and Differential Equations (MATH08063)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 8 (Year 2 Undergraduate) Availability Available to all students SCQF Credits 20 ECTS Credits 10 Summary A first several variable calculus course and a first methods course for differential equations. After a review of vector algebra, vector calculus is introduced, including gradient, divergence and curl functions. Double, triple, line, surface and volume integrals are discussed and practised. Green's Theorem, Stokes' theorem and divergence, (Gauss') theorem are distinct highlight. First order linear ordinary diff. eq. are solved by separation, using an integrating factor and numerically. Various solution methods for second¿order linear homogeneous equations are presented.The course ends with a discussion of the series expansion solutions Course description Week 1 : Vectors and vector functions. (Book 1, Chapter 10) Weeks 1-3 : Partial derivatives. (Book 1, Chapter 11) Weeks 4-5 : Multiple integrals. (Book 1, Chapter 12) Weeks 6-7 : Vector calculus. (Book 1, Chapter 13) Weeks 8-9 : 1st order differential equations. (Book 2, Chapters 1 and 2) Weeks 9-11 : 2nd order differential equations. (Book 2, Chapters 3 and 5)
 Pre-requisites Students MUST have passed: Calculus and its Applications (MATH08058) OR Accelerated Algebra and Calculus for Direct Entry (MATH08062) Students MUST have passed: Co-requisites Prohibited Combinations Students MUST NOT also be taking Engineering Mathematics 2A (SCEE08009) OR Engineering Mathematics 2B (SCEE08010) OR Linear Algebra and Several Variable Calculus (PHYS08042) Other requirements None
 Pre-requisites Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. High Demand Course? Yes
 Academic year 2021/22, Available to all students (SV1) Quota:  450 Course Start Semester 1 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 42, Seminar/Tutorial Hours 11, Summative Assessment Hours 3, Revision Session Hours 2, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 138 ) Additional Information (Learning and Teaching) Students must attain at least 40% overall to pass the course Assessment (Further Info) Written Exam 60 %, Coursework 40 %, Practical Exam 0 % Additional Information (Assessment) Coursework 40%, Examination 60% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) 2:00 Resit Exam Diet (August) 2:00
 On completion of this course, the student will be able to: Manipulate routine algebraic and numerical calculations, for example partial derivatives and derived functions, vectors and vector functions, double and triple integrals, line and surface integrals, to solve standard problems without explicit prompting.State, use and derive in good mathematical style the principal theoretical results of the course, e.g. critical points of functions in several variables, Stokes' theorem and Gauss' (divergence) theorem, to solve unseen problems which extend examples studied.Identify differential equations belonging to some standard classes and choose and apply the appropriate methods for their solution.
 Students are expected to have a personal copies of : Book 1: Essential Calculus , Early Transcendentals by James Stewart Book 2: Boyce's Elementary Differential Equations and Boundary Value Problems by William E. Boyce, Richard C. DiPrima and Douglas B Meade
 Graduate Attributes and Skills Not entered Keywords SVCDE
 Course organiser Dr Maximilian Ruffert Tel: (0131 6)50 5039 Email: M.Ruffert@ed.ac.uk Course secretary Mr Martin Delaney Tel: (0131 6)50 6427 Email: Martin.Delaney@ed.ac.uk
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