VECTOR CALCULUS

MAT2VCA

2021

Credit points: 15

Subject outline

Many quantities in the physical world can be represented by smoothly varying functions of position in two or three dimensions. This subject develops, with an emphasis on relevant calculations, the differential and integral calculus of scalar and vector fields in cartesian and curvilinear coordinates. Three important partial differential equations are introduced: the wave equation, the heat equation and Laplace's equation; to solve them, they are reduced to several ordinary differential equations by the technique of separation of variables. Laplace transforms are introduced as a technique for solving constant coefficient ordinary differential equations with discontinuous forcing terms, such as those which arise in electronics. Thus we generalize many of the techniques used in first year (to analyse functions of a single variable) to the several variable case, as most real-world systems depend crucially on multiple factors. (For engineering students: stage one competencies 1.2, 3.2 and 3.4 are developed.)

SchoolEngineering and Mathematical Sciences

Credit points15

Subject Co-ordinatorJoel Miller

Available to Study Abroad/Exchange StudentsYes

Subject year levelYear Level 2 - UG

Available as ElectiveNo

Learning ActivitiesN/A

Capstone subjectNo

Subject particulars

Subject rules

PrerequisitesMAT1CLA OR (MAT1CDE AND MAT1NLA)

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

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. Solve linear differential equations using the Laplace Transform technique.
02. Describe and classify features of a function of several variables, analysing them using graphical and computational techniques.
03. Apply the processes of calculus (differentiation and integration meaningfully to functions of several variables in rectangular and curvilinear coordinates.
04. Solve partial differential equations in appropriate coordinates using the technique of separation of variables.
05. Communicate your understanding (of vector calculus using both words and mathematical notation in a precise and succinct manner.

Subject options

Select to view your study options…

Start date between: and    Key dates

Bendigo, 2021, Semester 1, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Subject Instance Co-ordinatorMumtaz Hussain

Class requirements

LectureWeek: 10 - 22
Two 1.00 h lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

PracticalWeek: 10 - 22
Two 1.00 h practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Assessments

Assessment elementCommentsCategoryContributionHurdle% ILO*
Written test on Laplace Transforms (30 mins) (500 words equivalent)N/AN/AN/ANo10 SILO1
4x written assignments (250 words equivalent each)N/AN/AN/ANo20 SILO1, SILO2, SILO3, SILO4, SILO5
One 3-hour examination (3000 words equivalent)N/AN/AN/ANo70 SILO2, SILO3, SILO4, SILO5

Melbourne (Bundoora), 2021, Semester 1, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Subject Instance Co-ordinatorJoel Miller

Class requirements

LectureWeek: 10 - 22
Two 1.00 h lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

PracticalWeek: 10 - 22
Two 1.00 h practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Assessments

Assessment elementCommentsCategoryContributionHurdle% ILO*
Written test on Laplace Transforms (30 mins) (500 words equivalent)N/AN/AN/ANo10 SILO1
4x written assignments (250 words equivalent each)N/AN/AN/ANo20 SILO1, SILO2, SILO3, SILO4, SILO5
One 3-hour examination (3000 words equivalent)N/AN/AN/ANo70 SILO2, SILO3, SILO4, SILO5