Several Variable Calculus (U01477)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-2-SVC

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.

Entry Requirements

? Pre-requisites : Passes at C-grade or better in MAT-1-PCa, MAT-1-SEq, MAT-1-GCo, MAT-1-GTh, or permission of the Head of the School of Mathematics

? Prohibited combinations : MAT-2-mm3, MAT-2-mc3, MAT-2-mc4, MAT-2-me3, MAT-2-me4

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Year 2), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 2nd year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) 30 minutes per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
20/09/2006	12:10	13:00	Lecture Theatre 1, Ashworth Labs	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	KB
Lecture	Wednesday	12:10	13:00	KB

? Additional Class Information : Tutorials: Th at 1110 and 1210.

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.