ADVANCED CALCULUS AND CURVATURE

MAT3AC

2018

Credit points: 15

Subject outline

This subject unifies linear algebra and vector calculus from second year into the sort of calculus used in differential geometry and analysis. The central notion is that of manifolds, which is a generalization of curves and surfaces, and provides the mathematical context for understanding "space" in all of its manifestations. Topics include: the implicit and inverse function theorems, manifolds and tangent space, curvature and torsion for curves, intrinsic and extrinsic curvature for surfaces, and the Theorema Egregium of Gauss.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorYuri Nikolayevsky

Available to Study Abroad StudentsYes

Subject year levelYear Level 3 - UG

Exchange StudentsYes

Subject particulars

Subject rules

Prerequisites MAT2VCA

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Special conditionsN/A

Readings

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsAdvanced Calculus and CurvaturePrescribedY.Nikolayevsky, 2014LTU

Graduate capabilities & intended learning outcomes

01. Construct manifolds explicitly and implicitly, as well as their tangent spaces

Activities:
These are modelled in lectures, with reinforcment in practice classes and marked feedback through assignments
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)

02. Use MAPLE to graph manifolds and investigate mappings

Activities:
Guided exercises in practice classes, with marked feedback through assignments
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)

03. Correctly invoke the inverse and implicit function theorems in mathematical arguments

Activities:
Demonstrated in lectures, with reinforcment in practice classes and marked feedback through assignments
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)

04. Calculate the curvature of curves and surfaces

Activities:
Demonstrated in lectures, with reinforcment in practice classes and marked feedback through assignments
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)

05. Communicate your understanding (of manifolds) using both words and mathematical notation in a precise and succinct manner

Activities:
Written communication is demonstrated through lectures, with guidance in practice class and with marked feedback in assignments. Information and guidance is also provided to aid the writing of the essay.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)

Subject options

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Start date between: and    Key dates

Melbourne, 2018, Semester 2, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorYuri Nikolayevsky

Class requirements

Practical Week: 31 - 43
One 1.0 hours practical per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Lecture Week: 31 - 43
Two 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Assessments

Assessment elementComments% ILO*
Four written mathematics assignments (1000 words equivalent total)20 01, 02, 03, 04, 05
One 1000-1500 word essay10 05
One 2-hour written exam70 01, 03, 04, 05