mat3ac advanced calculus

ADVANCED CALCULUS AND CURVATURE

MAT3AC

2016

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-ordinatorDimetre Triadis

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

Learning resources

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:
Inquiry/ Research(Inquiry/ Research)
Creative Problem-solving(Creative Problem-solving)
Critical Thinking(Critical Thinking)
Discipline-specific GCs(Discipline-specific GCs)
Writing(Writing)

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:
Inquiry/ Research(Inquiry/ Research)
Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
Critical Thinking(Critical Thinking)
Creative Problem-solving(Creative Problem-solving)
Discipline-specific GCs(Discipline-specific GCs)

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:
Inquiry/ Research(Inquiry/ Research)
Writing(Writing)
Creative Problem-solving(Creative Problem-solving)
Critical Thinking(Critical Thinking)
Discipline-specific GCs(Discipline-specific GCs)

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:
Writing(Writing)
Discipline-specific GCs(Discipline-specific GCs)
Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
Creative Problem-solving(Creative Problem-solving)
Inquiry/ Research(Inquiry/ Research)
Critical Thinking(Critical Thinking)

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:
Writing(Writing)
Critical Thinking(Critical Thinking)
Discipline-specific GCs(Discipline-specific GCs)
Inquiry/ Research(Inquiry/ Research)
Creative Problem-solving(Creative Problem-solving)

Subject options

Select to view your study options…

Start date between: and    Key dates

Melbourne, 2016, Semester 2, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorDimetre Triadis

Class requirements

PracticalWeek: 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.

LectureWeek: 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 assignments2001, 02, 03, 04, 05
One 1000-1500 word essay1005
One 2-hour written exam7001, 03, 04, 05