## Handbook home

# Calculus 2 (MAST10006)

Undergraduate level 1Points: 12.5On Campus (Parkville)

About this subject

- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)

## Contact information

Please refer to the specific study period for contact information.

## Overview

Year of offer | 2017 |
---|---|

Subject level | Undergraduate Level 1 |

Subject code | MAST10006 |

Campus | Parkville |

Availability | Semester 1 Semester 2 |

Fees | Subject EFTSL, Level, Discipline & Census Date |

This subject will extend knowledge of calculus from school. Students are introduced to hyperbolic functions and their inverses, the complex exponential and functions of two variables. Techniques of differentiation and integration will be extended to these cases. Students will be exposed to a wider class of differential equation models, both first and second order, to describe systems such as population models, electrical circuits and mechanical oscillators. The subject also introduces sequences and series including the concepts of convergence and divergence.

Calculus topics include: intuitive idea of limits and continuity of functions of one variable, sequences, series, hyperbolic functions and their inverses, level curves, partial derivatives, chain rules for partial derivatives, directional derivative, tangent planes and extrema for functions of several variables. Complex exponential topics include: definition, derivative, integral and applications. Integration topics include: techniques of integration and double integrals. Ordinary differential equations topics include: first order (separable, linear via integrating factor) and applications, second order constant coefficient (particular solutions, complementary functions) and applications.

## Intended learning outcomes

Students completing this subject should be able to:

- calculate simple limits of a function of one variable;
- determine convergence and divergence of sequences and series;
- sketch and manipulate hyperbolic and inverse hyperbolic functions;
- evaluate integrals using trigonometric and hyperbolic substitutions, partial fractions, integration by parts and the complex exponential;
- find analytical solutions of first and second order ordinary differential equations, and use these equations to model some simple physical and biological systems;
- calculate partial derivatives and gradients for functions of two variables, and use these to find maxima and minima.

## Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;

- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;

- collaborative skills: the ability to work in a team; and

- time-management skills: the ability to meet regular deadlines while balancing competing commitments.

## Eligibility and requirements

### Prerequisites

A study score of at least 29 in VCE Specialist Mathematics 3/4, or equivalent, or one of

- MAST10005 Calculus 1
- MAST10007 Linear Algebra

### Corequisites

None

### Non-allowed subjects

Students may only gain credit for one of

- MAST10006 Calculus 2
- MAST10009 Accelerated Mathematics 2
- MAST10019 Calculus Extension Studies

Students may not enrol in MAST10005 Calculus 1 and MAST10006 Calculus 2 concurrently.

Bachelor of Science students are permitted to complete a maximum of three level-1 Mathematics and Statistics subjects. They are not permitted to complete all four of MAST10005, MAST10006, MAST10007 and MAST10010

### Core participation requirements

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

## Assessment

### Description

Four or five written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).

## Dates & times

- Semester 1
Principal coordinator Iwan Jensen Mode of delivery On Campus — Parkville Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week. Total time commitment 170 hours Teaching period 27 February 2017 to 28 May 2017 Last self-enrol date 10 March 2017 Census date 31 March 2017 Last date to withdraw without fail 5 May 2017 Assessment period ends 23 June 2017 ### Semester 1 contact information

**Email:**mangel@unimelb.edu.au ; ij@unimelb.edu.au - Semester 2
Principal coordinator Christine Mangelsdorf Mode of delivery On Campus — Parkville Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week. Total time commitment 170 hours Teaching period 24 July 2017 to 22 October 2017 Last self-enrol date 4 August 2017 Census date 31 August 2017 Last date to withdraw without fail 22 September 2017 Assessment period ends 17 November 2017 ### Semester 2 contact information

**Email:**mangel@unimelb.edu.au ; ij@unimelb.edu.au

## Time commitment details

Estimated total time commitment of 170 hours

## Further information

- Texts
### Prescribed texts

There are no specifically prescribed or recommended texts for this subject.

- Subject notes
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.

Students with a score of 40 or more in VCE Specialist Mathematics 3/4 are strongly encouraged to enrol in both

- MAST10008 Accelerated Mathematics 1
- MAST10009 Accelerated Mathematics 2

instead of both

- MAST10006 Calculus 2
- MAST10007 Linear Algebra

Students with a study score of 29 in VCE Specialist Mathematics 3/4 or equivalent, are eligible to enrol in MAST10005 Calculus 1, MAST10006 Calculus 2 or MAST10007 Linear Algebra. Such students should seek course advice before completing their enrolment.

- Related Handbook entries
This subject contributes to the following:

Type Name Course Bachelor of Biomedicine Course Bachelor of Environments Informal specialisation Environments Discipline subjects Major Discrete Mathematics / Operations Research Major Engineering Systems Major Environmental Science major Informal specialisation Selective subjects for B-BMED Major Statistics / Stochastic Processes Major Pure Mathematics Informal specialisation Science-credited subjects - new generation B-SCI and B-ENG. Major Spatial Systems Informal specialisation Bachelor of Design Elective Subjects Major Applied Mathematics Breadth track Chemical Engineering Breadth track Electrical Engineering Breadth track Mechanical Engineering Breadth track Mathematics and Statistics Breadth track Mathematics for Economics - Breadth options
This subject is available as breadth in the following courses:

- Available through the Community Access Program
### About the Community Access Program (CAP)

This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.

Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.