# CALCULUS AND DIFFERENTIAL EQUATIONS

MAT1CDE

2017

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).)

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorNarwin Perkal

Subject year levelYear Level 1 - UG

Exchange StudentsYes

## Subject particulars

### Subject rules

Prerequisites VCE Mathematical Methods 3/4 or equivalent

Co-requisitesN/A

Incompatible subjects MAT1CNS, MAT1CPE, MAT1CLA, MAT1CA, MAT1CB

Equivalent subjectsN/A

Special conditionsN/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.
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.
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.
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.
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.
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.
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Critical Thinking (Critical Thinking)
Writing (Writing)
Discipline-specific GCs (Discipline-specific GCs)
Creative Problem-solving (Creative Problem-solving)

## Subject options

Select to view your study options…

Start date between: and    Key dates

## Bendigo, 2017, Semester 2, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorMumtaz Hussain

### Class requirements

Lecture Week: 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.

Practical Week: 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

3 hour examHurdle requirement: To pass the subject, a pass in the examination is mandatory.70 01, 02, 03, 04, 05, 06
5 assignments (typically 3-4 pages each)15 01, 02, 03, 04, 06
5 online diagnostic tasks15 01, 02, 03, 04, 05

## Melbourne, 2017, Semester 2, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorNarwin Perkal

### Class requirements

Lecture Week: 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.

Practical Week: 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.