# 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.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorNarwin Perkal

Subject year levelYear Level 4 - UG/Hons/1st Yr PG

Exchange StudentsNo

## Subject particulars

### Subject rules

Prerequisites Students must be admitted in SMDS and require coordinator's approval.

Co-requisitesN/A

Incompatible subjects MAT1CNS, MAT1CPE, MAT1CLA, MAT1CA, MAT1CB, MAT1CDE

Equivalent subjectsN/A

Special conditionsN/A

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsSurvival Skills for Tertiary MathsPrescribed2017Department of Mathematics and Statistics, La Trobe University
ReadingsCalculus and Differential EquationsPrescribed2017Department 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.

## Subject options

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Start date between: and    Key dates

## Melbourne, 2018, Semester 2, Day

### Overview

Online enrolmentNo

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.