CALCULUS AND DIFFERENTIAL EQUATIONS
MAT1CDE
2016
Credit points: 15
Subject outline
In this subject, students learn and apply mathematical concepts and develop skills that provide a foundation for all studies requiring a knowledge of calculus. Students refine and extend their knowledge of the concepts and techniques of differentiation and integration and move on to the notions of differential equations and modelling the real world. Techniques for solving first order separable and first and second order linear differential equations are covered together 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. Students will develop reasoning skills and the ability to clearly present their written arguments. They are strongly encouraged to practice verbal communication of ideas by working in small groups. (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: Narwin Perkal
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:
- Creative Problem-solving(Creative Problem-solving)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Critical Thinking(Critical Thinking)
- Discipline-specific GCs(Discipline-specific GCs)
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:
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
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:
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Discipline-specific GCs(Discipline-specific GCs)
- Creative Problem-solving(Creative Problem-solving)
- Critical Thinking(Critical Thinking)
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:
- Critical Thinking(Critical Thinking)
- Discipline-specific GCs(Discipline-specific GCs)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
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:
- Discipline-specific GCs(Discipline-specific GCs)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Critical Thinking(Critical Thinking)
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:
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Critical Thinking(Critical Thinking)
- Writing(Writing)
- Discipline-specific GCs(Discipline-specific GCs)
- Creative Problem-solving(Creative Problem-solving)
Bendigo, 2016, Semester 2, Day
Overview
Online enrolment: Yes
Maximum enrolment size: N/A
Enrolment information:
Subject Instance Co-ordinator: Simon Smith
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 | 70 | 01, 02, 03, 04, 05, 06 | |
| 5 assignments (typically 3-4 pages each) | 15 | 01, 02, 03, 04, 06 | |
| 5 online diagnostic tasks | Hurdle requirement: Students will be required to achieve a mark of at least 40% on the exam, as well as an overall mark of at least 50%, in order to pass this subject. | 15 | 01, 02, 03, 04, 05 |
Melbourne, 2016, 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 | 70 | 01, 02, 03, 04, 05, 06 | |
| 5 assignments (typically 3-4 pages each) | 15 | 01, 02, 03, 04, 06 | |
| 5 online diagnostic tasks | Hurdle requirement: Students will be required to achieve a mark of at least 40% on the exam, as well as an overall mark of at least 50%, in order to pass this subject. | 15 | 01, 02, 03, 04, 05 |