ADVANCED CALCULUS AND CURVATURE

MAT3AC

2020

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.

School: Engineering and Mathematical Sciences (Pre 2022)

Credit points: 15

Subject Co-ordinator: Yuri Nikolayevsky

Available to Study Abroad/Exchange Students: Yes

Subject year level: Year Level 3 - UG

Exchange Students: No

Available as Elective: No

Learning Activities: N/A

Capstone subject: Yes

Subject particulars

Subject rules

Prerequisites: MAT2VCA

Co-requisites: N/A

Incompatible subjects: N/A

Equivalent subjects: N/A

Quota Management Strategy: N/A

Quota-conditions or rules: N/A

Special conditions: N/A

Minimum credit point requirement: N/A

Assumed knowledge: N/A

Learning resources

Advanced Calculus and Curvature

Resource Type: Book

Resource Requirement: Prescribed

Author: Y.Nikolayevsky

Year: 2014

Edition/Volume: N/A

Publisher: LTU

ISBN: N/A

Chapter/article title: N/A

Chapter/issue: N/A

URL: N/A

Other description: N/A

Source location: N/A

Career Ready

Career-focused: No

Work-based learning: No

Self sourced or Uni sourced: N/A

Entire subject or partial subject: N/A

Total hours/days required: N/A

Location of WBL activity (region): N/A

WBL addtional requirements: N/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

COMMUNICATION - Communicating and Influencing

INQUIRY AND ANALYSIS - Research and Evidence-Based Inquiry

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

Melbourne (Bundoora), 2020, Semester 2, Day

Overview

Online enrolment: Yes

Maximum enrolment size: N/A

Enrolment information: N/A

Subject Instance Co-ordinator: Yuri Nikolayevsky

Class requirements

LectureWeek: 31 - 43
Two 1.00 hour lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

PracticalWeek: 31 - 43
One 1.00 hour practical per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Assessments

Assessment element	Comments	Category	Contribution	Hurdle	%	ILO*
Four written mathematics assignments (1000 words equivalent total)	N/A	N/A	N/A	No	20	SILO1, SILO2, SILO3, SILO4, SILO5
One 1000-1500 word essay	N/A	N/A	N/A	No	10	SILO5
One 2-hour written exam	N/A	N/A	N/A	No	70	SILO1, SILO3, SILO4, SILO5