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DRPS : Course Catalogue : School of Mathematics : Mathematics

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

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryA 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)
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Calculus and its Applications (MATH08058) OR Accelerated Algebra and Calculus for Direct Entry (MATH08062)
Students MUST have passed:
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
Information for Visiting Students
Pre-requisitesVisiting 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
Course Delivery Information
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
Learning Outcomes
On completion of this course, the student will be able to:
  1. 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.
  2. 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.
  3. Identify differential equations belonging to some standard classes and choose and apply the appropriate methods for their solution.
Reading List
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

Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Maximilian Ruffert
Tel: (0131 6)50 5039
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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