mat2vca vector calculus
VECTOR CALCULUS
MAT2VCA
2017
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 Co-ordinatorPhilip Broadbridge
Available to Study Abroad StudentsYes
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
Readings
| Resource Type | Title | Resource Requirement | Author and Year | Publisher |
|---|---|---|---|---|
| Readings | Printed subject text available from University Bookshop | Prescribed | . | . |
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.
- Related graduate capabilities and elements:
- Writing(Writing)
- Discipline-specific GCs(Discipline-specific GCs)
- Creative Problem-solving(Creative Problem-solving)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
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.
- Related graduate capabilities and elements:
- Critical Thinking(Critical Thinking)
- Discipline-specific GCs(Discipline-specific GCs)
- Writing(Writing)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
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.
- Related graduate capabilities and elements:
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Writing(Writing)
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
- Creative Problem-solving(Creative Problem-solving)
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.
- Related graduate capabilities and elements:
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
- Writing(Writing)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
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.
- Related graduate capabilities and elements:
- Writing(Writing)
Subject options
Select to view your study options…
Bendigo, 2017, Semester 1, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorChristopher Lenard
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
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| Written test on Laplace Transforms (30 mins) | 10 | 01 | |
| fortnightly written assignments | 20 | 01, 02, 03, 04, 05 | |
| one 2.5-hour examination | 70 | 02, 03, 04, 05 |
Melbourne, 2017, Semester 1, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorPhilip Broadbridge
Class requirements
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.
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.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| Written test on Laplace Transforms (30 mins) | 10 | 01 | |
| fortnightly written assignments | 20 | 01, 02, 03, 04, 05 | |
| one 2.5-hour examination | 70 | 02, 03, 04, 05 |