CALCULUS AND DIFFERENTIAL EQUATIONS
MAT1CDE
2019
Credit points: 15
Subject outline
Students will learn and apply mathematical concepts and develop skills that provide a foundation for all studies requiring knowledge of calculus. Students refine and extend their knowledge of the concepts and techniques of calculus and move on to the ideas of differential equations and modelling the real world. The power and limitations of models to make predictions about ecological and economic sustainability are explored. First order separable and first and second order linear differential equations are covered along with some approximation techniques. An active learning approach is used engaging students in solving mathematical problems and exploring the detail of mathematical concepts so they can be appropriately applied. Reasoning skills and the ability to clearly present written arguments will be developed and verbal communication skills are practiced through group-work and interaction with staff. (Engineering students will work to achieve the stage one competencies 1.2 (conceptual understanding of the underpinning mathematics, numerical analysis and statistics), 3.2 (effective written communication) and 3.4 (management of self).)
School: School Engineering&Mathematical Sciences
Credit points: 15
Subject Co-ordinator: Toen Castle
Available to Study Abroad Students: Yes
Subject year level: Year Level 1 - UG
Exchange Students: Yes
Subject particulars
Subject rules
Prerequisites: VCE Mathematical Methods 3/4 or equivalent
Co-requisites: N/A
Incompatible subjects: MAT1CNS, MAT1CPE, MAT1CLA, MAT1CA, MAT1CB
Equivalent subjects: N/A
Special conditions: N/A
Graduate capabilities & intended learning outcomes
01. Apply basic techniques of differentiation and explain the relationship between differentiation and slopes of tangents.
- Activities:
- Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Quantitative Literacy)
02. Identify and apply basic techniques of integration, and utilise the relationship between integration and signed areas under curves to calculate basic integrals.
- Activities:
- Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Quantitative Literacy)
03. Identify and apply appropriate techniques to solve first and second order ordinary differential equations.
- Activities:
- Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Quantitative Literacy)
04. Use Taylor Polynomials to find polynomial approximations to functions near 0 and use Taylor's theorem to determine the accuracy of the approximations.
- Activities:
- Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Quantitative Literacy)
05. Use numerical techniques to find approximations of solutions to differential equations.
- Activities:
- Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Quantitative Literacy)
06. Present mathematical thinking in written form in a meaningful and succinct way using both words and mathematical notation.
- Activities:
- Emphasis is placed on this in lectures and practice classes and assignments have specifically allocated marks for, and feedback on improvements to, written mathematical communication.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Quantitative Literacy)
07. Draw conclusions from mathematical models representing real-world phenomena.
- Activities:
- Lectures and practice classes. Assessed in assignments and exam.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Quantitative Literacy)
Bendigo, 2019, Semester 2, Day
Overview
Online enrolment: Yes
Maximum enrolment size: N/A
Enrolment information:
Subject Instance Co-ordinator: Toen Castle
Class requirements
LectureWeek: 31 - 43
Two 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.
PracticalWeek: 31 - 43
Two 1.0 hours practical per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| 3 hour exam (3000 words equivalent) | Hurdle requirement: To pass the subject, a pass in the examination is mandatory. | 70 | 01, 02, 03, 04, 05, 06, 07 |
| 5 assignments (typically 3-4 pages each) (1250 words equivalent) | 15 | 01, 02, 03, 04, 06, 07 | |
| 5 online diagnostic tasks (250 words equivalent) | 15 | 01, 02, 03, 04, 05 |
Melbourne, 2019, Semester 2, Day
Overview
Online enrolment: Yes
Maximum enrolment size: N/A
Enrolment information:
Subject Instance Co-ordinator: Narwin Perkal
Class requirements
LectureWeek: 31 - 43
Two 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.
PracticalWeek: 31 - 43
Two 1.0 hours practical per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| 3 hour exam (3000 words equivalent) | Hurdle requirement: To pass the subject, a pass in the examination is mandatory. | 70 | 01, 02, 03, 04, 05, 06, 07 |
| 5 assignments (typically 3-4 pages each) (1250 words equivalent) | 15 | 01, 02, 03, 04, 06, 07 | |
| 5 online diagnostic tasks (250 words equivalent) | 15 | 01, 02, 03, 04, 05 |