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
|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
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)
Information for Visiting Students
|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?
Course Delivery Information
|Academic year 2019/20, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Additional Information (Learning and Teaching)
Students must pass exam and course overall.
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
||Hours & Minutes
|Main Exam Diet S1 (December)||3:00|
|Resit Exam Diet (August)||3:00|
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 :|
Essential Calculus , Early Transcendentals by James Stewart
Boyce's Elementary Differential Equations and Boundary Value Problems by William E. Boyce, Richard C. DiPrima and Douglas B Meade
|Graduate Attributes and Skills
|Course organiser||Dr Maximilian Ruffert
Tel: (0131 6)50 5039
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427