CALCULUS AND DIFFERENTIAL EQUATIONS

MAT1CDE

2018

Credit points: 15

This subject addresses La Trobe's Sustainability Thinking Essential. Sustainability Thinking entails deep appreciation of how the choices we make affects the natural, economic, social, political and cultural systems — now and in the future.

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).)

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorNarwin Perkal

Available to Study Abroad StudentsYes

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.
Related graduate capabilities and elements:
Literacies and Communication Skills

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

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

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

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

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

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

Subject options

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Start date between: and    Key dates

Bendigo, 2018, 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

Assessment elementComments% 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, 2018, 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.

Assessments

Assessment elementComments% 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