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 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)
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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? |
Yes |
Course Delivery Information
|
| Academic year 2024/25, Available to all students (SV1)
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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.
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Reading List
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
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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 |
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