VECTOR CALCULUS

MAT2VCA

2020

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.)

School: Engineering and Mathematical Sciences (Pre 2022)

Credit points: 15

Subject Co-ordinator: Joel Miller

Available to Study Abroad/Exchange Students: Yes

Subject year level: Year Level 2 - UG

Exchange Students: No

Available as Elective: No

Learning Activities: N/A

Capstone subject: No

Subject particulars

Subject rules

Prerequisites: MAT1CLA OR (MAT1NLA AND MAT1CDE)

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

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

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.

Bendigo, 2020, Semester 1, Day

Overview

Online enrolment: Yes

Maximum enrolment size: N/A

Enrolment information: N/A

Subject Instance Co-ordinator: Mumtaz Hussain

Class requirements

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

Assessments

Assessment element	Comments	Category	Contribution	Hurdle	%	ILO*
Written test on Laplace Transforms (30 mins) (500 words equivalent)	N/A	N/A	N/A	No	10	SILO1
4x written assignments (250 words equivalent each)	N/A	N/A	N/A	No	20	SILO1, SILO2, SILO3, SILO4, SILO5
One 3-hour examination (3000 words equivalent)	N/A	N/A	N/A	No	70	SILO2, SILO3, SILO4, SILO5

Melbourne (Bundoora), 2020, Semester 1, Day