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Calculus 2: Advanced (MAST10021)
Undergraduate level 1Points: 12.5On Campus (Parkville)
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 2
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
Availability | Semester 2 |
---|---|
Fees | Look up fees |
This subject covers the same material as MAST10006 Calculus 2, but to a greater depth including a greater emphasis on mathematical rigour and proof.
Students are introduced the complex exponential function, even and odd functions and functions of two or more 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. In addition to the intuitive understanding of convergence, students will see the mathematical definition of convergence.
Calculus topics include: 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 limits of functions 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 physical and biological systems
- calculate partial derivatives and gradients for functions of two or more variables, and use these to find maxima and minima
- be able to construct a simple mathematical proof
Generic skills
- 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
- time-management skills: the ability to meet regular deadlines while balancing competing commitments
Last updated: 15 February 2024
Eligibility and requirements
Prerequisites
Required subjects
A study score of at least 36 in VCE Specialist Mathematics 3/4, or equivalent
OR
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10022 | Linear Algebra: Advanced | Semester 1 (On Campus - Parkville) |
12.5 |
OR
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10005 | Calculus 1 |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
with a mark of at least 80%
OR
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10007 | Linear Algebra |
Summer Term (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
with a mark of at least 75%
OR
MAST10018: Linear Algebra Extension Studies
with a mark of at least 75%
Corequisites
None
Non-allowed subjects
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10006 | Calculus 2 |
Semester 1 (On Campus - Parkville)
Summer Term (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
MAST10009 | Accelerated Mathematics 2 | Semester 2 (On Campus - Parkville) |
12.5 |
MAST10019 Calculus Extension Studies
Inherent requirements (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
Last updated: 15 February 2024
Assessment
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
Description | Timing | Percentage |
---|---|---|
Eight to ten assignments (written or online) due at regular intervals during semester (approximately 30 hours total, worth 20%). Up to one third of the assignment based assessment will be completed online.
| Throughout the semester | 20% |
3-hour written examination in the examination period (80%).
| During the assessment period | 80% |
Additional details
This Dual-Delivery subject has On Campus assessment components.
Last updated: 15 February 2024
Dates & times
- Semester 2
Principal coordinator Volker Schlue 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 3 August 2020 to 1 November 2020 Last self-enrol date 14 August 2020 Census date 21 September 2020 Last date to withdraw without fail 16 October 2020 Assessment period ends 27 November 2020 Semester 2 contact information
Time commitment details
Estimated total time commitment of 170 hours
Additional delivery details
This Dual-Delivery subject has On Campus assessment components.
Last updated: 15 February 2024
Further information
- Texts
Prescribed texts
There are no specifically prescribed or recommended texts for this subject.
- Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Arts
- Bachelor of Commerce
- Bachelor of Design
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- 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.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 15 February 2024