# VECTOR CALCULUS

MAT2VCA

2019

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.)

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject year levelYear Level 2 - UG

Exchange StudentsYes

## Subject particulars

### Subject rules

Prerequisites MAT1CLA or (MAT1NLA and MAT1CDE)

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Special conditionsN/A

## Learning resources

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsPrinted subject text available from University BookshopPrescribed..

## Graduate capabilities & intended learning outcomes

01. Solve linear differential equations using the Laplace Transform technique.

Activities:
Worked examples are presented in three lectures and three practice classes are devoted to practising this technique.

02. Describe and classify features of a function of several variables, analysing them using graphical and computational techniques.

Activities:
Theory and worked examples are presented in five lectures, and in the associated practice classes, students draw diagrams and perform calculations to analyse functions of several variables.

03. Apply the processes of calculus (differentiation and integration) meaningfully to functions of several variables in rectangular and curvilinear coordinates.

Activities:
In twelve lectures, theory and worked examples are developed. In the associated practice classes, students perform calculations and answer questions requiring conclusions and interpretations of their calculations.

04. Solve partial differential equations in appropriate coordinates using the technique of separation of variables.

Activities:
The technique and applications are discussed in six lectures. In the associated practice classes, students practice the technique in several two and three dimensional coordinate systems.

05. Communicate your understanding (of vector calculus) using both words and mathematical notation in a precise and succinct manner.

Activities:
Mathematical writing is modelled in lectures and by use of model solutions to practice classes and assignments. Feedback is given on marked assignments on student's progress towards this ILO.

## Subject options

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Start date between: and    Key dates

## Bendigo, 2019, Semester 1, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorMumtaz Hussain

### Class requirements

LectureWeek: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

PracticalWeek: 10 - 22
Two 1.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

### Assessments

Written test on Laplace Transforms (30 mins)1001
Fortnightly written assignments (1500 word equivalent total)2001, 02, 03, 04, 05
One 2.5-hour examination7002, 03, 04, 05

## Melbourne, 2019, Semester 1, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

### Class requirements

LectureWeek: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

PracticalWeek: 10 - 22
Two 1.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.