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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2012/2013
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Several Variable Calculus (MATH08006)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) Credits10
Home subject areaMathematics Other subject areaSpecialist Mathematics & Statistics (Year 2)
Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic?No
Course descriptionCore 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Practical Calculus (MATH08001) AND Solving Equations (MATH08002) AND Geometry & Convergence (MATH08003) AND Group Theory: An Introduction to Abstract Mathematics (MATH08004)) OR ( Mathematical Methods 1 (MATH08029) AND Applicable Mathematics 1 (MATH08027) AND Mathematical Methods 2 (MATH08032) AND Applicable Mathematics 2 (MATH08031)) OR ( Mathematics for Informatics 1a (MATH08046) AND Mathematics for Informatics 1b (MINF08001) AND Mathematics for Informatics 2a (MINF08002) AND Mathematics for Informatics 2b (MATH08047)) OR ( Applicable Mathematics 1+2 (Physics) (MATH08049) AND Mathematical Methods 1+2 (Physics) (MATH08050))
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Mathematical Methods 3 (Phys Sci) (MATH08016) OR Mathematics for Chem Eng 3 (MATH08019) OR Mathematics for Chem Eng 4 (MATH08020) OR Mathematics for Elec/Mech Eng 3 (MATH08033) OR Mathematics for Elec/Mech Eng 4 (MATH08034)
Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Not being delivered
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.
Assessment Information
Coursework (which may include a Project): 15%; Degree Examination: 85%.
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
KeywordsSVC
Contacts
Course organiserDr Nikolaos Bournaveas
Tel: (0131 6)50 5063
Email: N.Bournaveas@ed.ac.uk
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk
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© Copyright 2012 The University of Edinburgh - 31 August 2012 4:17 am