mat3ac advanced calculus
ADVANCED CALCULUS AND CURVATURE
MAT3AC
2017
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
Learning resources
Readings
| Resource Type | Title | Resource Requirement | Author and Year | Publisher |
|---|---|---|---|---|
| Readings | Advanced Calculus and Curvature | Prescribed | Y.Nikolayevsky, 2014 | LTU |
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
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Melbourne, 2017, Semester 2, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorYuri Nikolayevsky
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 element | Comments | % | ILO* |
|---|---|---|---|
| Four written mathematics assignments | 20 | 01, 02, 03, 04, 05 | |
| One 1000-1500 word essay | 10 | 05 | |
| One 2-hour written exam | 70 | 01, 03, 04, 05 |