ADVANCED CALCULUS AND CURVATURE

MAT3AC

2021

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 objects of study are curves and surfaces in the space and differentiable maps. Topics include: the implicit and inverse function theorems, tangent space and tangent map, curvature and torsion for curves, intrinsic and extrinsic curvature for surfaces, and the Theorema Egregium of Gauss.

SchoolEngineering and Mathematical Sciences

Credit points15

Subject Co-ordinatorYuri Nikolayevsky

Available to Study Abroad/Exchange StudentsYes

Subject year levelYear Level 3 - UG

Available as ElectiveNo

Learning ActivitiesN/A

Capstone subjectYes

Subject particulars

Subject rules

PrerequisitesMAT2VCA

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Quota Management StrategyN/A

Quota-conditions or rulesN/A

Special conditionsN/A

Minimum credit point requirementN/A

Assumed knowledgeN/A

Readings

Advanced Calculus and Curvature

Resource TypePrescribed

Resource RequirementN/A

AuthorY.Nikolayevsky

Year2014

Edition/VolumeN/A

PublisherLTU

ISBNN/A

Chapter/article titleN/A

Chapter/issueN/A

URLN/A

Other descriptionN/A

Source locationN/A

Career Ready

Career-focusedNo

Work-based learningNo

Self sourced or Uni sourcedN/A

Entire subject or partial subjectN/A

Total hours/days requiredN/A

Location of WBL activity (region)N/A

WBL addtional requirementsN/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

Intended Learning Outcomes

01. Construct curves and surfaces explicitly and implicitly, as well as their tangent and normal spaces
02. Apply the apparatus of calculus and differential equations to calculate geometric invariants and to derive equations of geodesics.
03. Correctly invoke the inverse and implicit function theorems in mathematical arguments
04. Calculate the curvature of curves and surfaces
05. Communicate your understanding using both words and mathematical notation in a precise and succinct manner

Subject options

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Start date between: and    Key dates

Melbourne (Bundoora), 2021, Semester 2, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Subject Instance Co-ordinatorYuri Nikolayevsky

Class requirements

Lecture Week: 30 - 42
Two 1.00 h lecture per week on weekdays during the day from week 30 to week 42 and delivered via face-to-face.

Practical Week: 30 - 42
One 1.00 h practical per week on weekdays during the day from week 30 to week 42 and delivered via face-to-face.

Assessments

Assessment elementCommentsCategoryContributionHurdle% ILO*

Four written mathematics assignments (1000 words equivalent total)

N/AAssignmentIndividualNo20 SILO1, SILO2, SILO3, SILO4, SILO5

One 1000-1500 word essay

N/AOtherIndividualNo10 SILO5

One 2-hour written exam

N/ACentral examIndividualNo70 SILO1, SILO3, SILO4, SILO5