Undergraduate Course: Several Variable Calculus (MATH08006)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Year 2) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | Core second year course for Honours Degrees in Mathematics and/or Statistics.
Syllabus summary: Functions from Rm to Rn, partial derivatives, chain rule. Curves, velocity, tangent lines. Integration over domains in R2 and R3. Standard curvilinear coordinate systems. Green's Theorem in the plane. Integration over curves and surfaces. Taylor series, stationary points. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
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| Delivery period: 2012/13 Semester 1, Available to all students (SV1)
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WebCT enabled: Yes |
Quota: 277 |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | Ashworth Th 1 | 1-11 | | | 12:10 - 13:00 | | | | King's Buildings | Lecture | Ashworth Th 1 | 1-11 | 12:10 - 13:00 | | | | |
| First Class |
First class information not currently available |
| Additional information |
Tutorials: Th at 1000, 1110 and 1210. |
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S1 (December) | Several Variable Calculus | 2:00 | | | | Resit Exam Diet (August) | | 2:00 | | |
Summary of Intended Learning Outcomes
1. Using Maple to plot surfaces, using both cartesian and polar co-ordinate presentations. Interpret Maple output. Sketch some surfaces by hand.
2. Sketching level curves by hand.
3. Calculating first and second order partial derivatives from formulae, and from first principles.
4. Calculating the gradient function, and the derivative map.
5. Using the chain rule to calculate partial derivatives of composite functions, in both scalar and matrix forms.
6. Calculating the Taylor approximation of a function, up to the quadratic terms.
7. Identifying local extrema and critical points. Use the Hessian matrix to investigate the form of a surface at a critical point. Identify when the Hessian is positive definite, in two and three dimensions, using the subdeterminant criterion.
8. Using the Lagrange multiplier method to find local extrema of functions, under one constraint only.
9. Calculating easy double integrals. Change the order of integration in double integrals, for easy regions.
10. Calculating arc-length and surface areas for easy functions. Use Green's Theorem in the plane.
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Assessment Information
Coursework (which may include a Project): 15%; Degree Examination: 85%.
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Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | SVC |
Contacts
| Course organiser | Dr Nikolaos Bournaveas
Tel: (0131 6)50 5063
Email: |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: |
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© Copyright 2012 The University of Edinburgh - 6 March 2012 6:15 am
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