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Calculus 2 (MAST10006)

Undergraduate level 1Points: 12.5On Campus (Parkville)

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Year of offer2019
Subject levelUndergraduate Level 1
Subject codeMAST10006
Semester 1
Semester 2
FeesSubject 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


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

  • MAST10005 Calculus 1
  • MAST10007 Linear Algebra



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



Eight to ten assignments (written or online) 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%). Up to one third of the assignment based assessment will be completed online.

Dates & times

  • Semester 1
    Principal coordinatorDiarmuid Crowley
    Mode of deliveryOn Campus — Parkville
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week.
    Total time commitment170 hours
    Teaching period 4 March 2019 to 2 June 2019
    Last self-enrol date15 March 2019
    Census date31 March 2019
    Last date to withdraw without fail10 May 2019
    Assessment period ends28 June 2019
  • Semester 2
    Principal coordinatorAnthony Morphett
    Mode of deliveryOn Campus — Parkville
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week.
    Total time commitment170 hours
    Teaching period29 July 2019 to 27 October 2019
    Last self-enrol date 9 August 2019
    Census date31 August 2019
    Last date to withdraw without fail27 September 2019
    Assessment period ends22 November 2019

    Semester 2 contact information

Time commitment details

Estimated total time commitment of 170 hours

Further information

Last updated: 12 June 2019