CALCULUS AND DIFFERENTIAL EQUATIONS
MAT4CDE
2018
Credit points: 15
Subject outline
Analysing and interpreting big data sets requires an extensive range of mathematical skills. In this subject, 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 and professionally present their written arguments.
School: School Engineering&Mathematical Sciences
Credit points: 15
Subject Co-ordinator: Narwin Perkal
Available to Study Abroad Students: No
Subject year level: Year Level 4 - UG/Hons/1st Yr PG
Exchange Students: No
Subject particulars
Subject rules
Prerequisites: Students must be admitted in SMDS and require coordinator's approval.
Co-requisites: N/A
Incompatible subjects: MAT1CNS, MAT1CPE, MAT1CLA, MAT1CA, MAT1CB, MAT1CDE
Equivalent subjects: N/A
Special conditions: N/A
Learning resources
Readings
| Resource Type | Title | Resource Requirement | Author and Year | Publisher |
|---|---|---|---|---|
| Readings | Survival Skills for Tertiary Maths | Prescribed | 2017 | Department of Mathematics and Statistics, La Trobe University |
| Readings | Calculus and Differential Equations | Prescribed | 2017 | Department of Mathematics and Statistics, La Trobe University |
Graduate capabilities & intended learning outcomes
01. Apply 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.
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.
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.
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.
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.
06. Discuss the application of the techniques of calculus and mathematical modelling to data science.
- Activities:
- Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Assessment task (essay) provides opportunity to research and discuss applications.
07. Present mathematical thinking in written form in a professional, meaningful and succinct way with emphasis on requirements for report and paper writing.
- 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.
Melbourne, 2018, Semester 2, Day
Overview
Online enrolment: No
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* |
|---|---|---|---|
| Two 1.5 hour exams (equivalent to 3000 words) | Hurdle requirement: To pass the subject, a pass in the examination is mandatory. | 65 | 01, 02, 03, 04, 05, 06, 07 |
| 5 assignments (typically 3-4 pages each, equivalent to 400 words each) | 20 | 01, 02, 03, 04, 06, 07 | |
| Essay (1500 words) | 15 | 01, 02, 03, 04, 05, 06, 07 |