Undergraduate Course: Several Variable Calculus and Differential Equations (MATH08063)
Course Outline
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 13 : Partial derivatives. (Book 1, Chapter 11)
Weeks 45 : Multiple integrals. (Book 1, Chapter 12)
Weeks 67 : Vector calculus. (Book 1, Chapter 13)
Weeks 89 : 1st order differential equations. (Book 2, Chapters 1 and 2)
Weeks 911 : 2nd order differential equations. (Book 2, Chapters 3 and 5)

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2023/24, Available to all students (SV1)

Quota: 320 
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)  Several Variable Calculus and Differential Equations (MATH08063)  2:00   Resit Exam Diet (August)  Several Variable Calculus and Differential Equations (MATH08063)  2:00  
Learning Outcomes
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.

Reading List
Students are expected to have Students are expected to have access to 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 
Keywords  SVCDE 
Contacts
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 

