Calculus 2: Advanced (MAST10021)

Undergraduate level 1Points: 12.5On Campus (Parkville)

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Overview

Availability
Semester 2
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This subject covers the same material as MAST10006 Calculus 2, but to a greater depth and with a greater emphasis on concepts, mathematical rigour, and proofs.

Students are introduced to functions of several variables, the notion of a limit, and properties of continuous functions. Moreover, level curves, partial derivatives, the chain rule, directional derivatives, tangent planes and extrema for functions of several variables are discussed.

For functions of one variable, the concepts of differentiation and integration are reviewed, and the Fundamental Theorem of Calculus is presented. Integration by parts, and substitution are covered as the main methods of integration.

The subject also exposes students to ordinary differential equations. In particular, linear differential equations of both first and second order are discussed, as well as separable first order equations. Several special functions, such as the hyperbolic functions, and their inverses are covered in this context. Applications include the description of population models, and electrical circuits and mechanical oscillators.

The subject also introduces the idea of approximating functions by polynomials. In particular, Taylor polynomials for functions of one variable are discussed, and Taylor's theorem is presented.

In addition, the subject introduces infinite sequences and series, and the concepts of convergence and divergence. In addition to the intuitive understanding of convergence, students will see the mathematical definition of convergence.

Finally complex functions, and complex power series are introduced. In particular, the complex exponential function, and its properties are discussed.

Intended learning outcomes

Students completing this subject should be able to:

  • determine limits of functions of one or several variables
  • apply theorems about continuity to investigate functions
  • determine convergence and divergence of sequences and series
  • sketch and manipulate hyperbolic and inverse hyperbolic functions
  • evaluate integrals using integration by parts and substitution, in particular using trigonometric and hyperbolic substitutions, and partial fractions
  • find solutions of first and second order ordinary differential equations, and use these equations to model some physical and biological systems
  • compute Taylor polynomials of functions of one variable
  • calculate partial derivatives and gradients for functions of two or more variables, and use these to find maxima and minima
  • write 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: 30 January 2025

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
MAST10005 Calculus 1 No longer available

with a mark of at least 80%

OR

Code Name Teaching period Credit Points
MAST10007 Linear Algebra No longer available

with a mark of at least 75%

OR

Code Name Teaching period Credit Points
No longer available

with a mark of at least 75%

OR

Code Name Teaching period Credit Points
MAST10022 Linear Algebra: Advanced No longer available

Corequisites

None

Non-allowed subjects

Code Name Teaching period Credit Points
MAST10006 Calculus 2 No longer available
MAST10009 Accelerated Mathematics 2 No longer available

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: 30 January 2025

Assessment

DescriptionTimingPercentage

Six to eight assignments (written or online) due at regular intervals during semester (approximately 24 hours total, worth 15%). Up to one half of the assignment based assessment will be completed online.

  • 800 words (equivalent)
During the teaching period15%

A written mid-semester test

  • 45 minutes
Mid semester15%

3-hour written examination in the examination period (70%).

  • 3 hours
During the assessment period70%

Additional details

 

 

 

Last updated: 30 January 2025

Dates & times

  • Semester 2
    CoordinatorChenyan Wu
    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 period22 July 2024 to 20 October 2024
    Last self-enrol date 2 August 2024
    Census date 2 September 2024
    Last date to withdraw without fail20 September 2024
    Assessment period ends15 November 2024

    Semester 2 contact information

    chenyan.wu@unimelb.edu.au

Time commitment details

Estimated total time commitment of 170 hours

What do these dates mean

Visit this webpage to find out about these key dates, including how they impact on:

  • Your tuition fees, academic transcript and statements.
  • And for Commonwealth Supported students, your:
       -  Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
     

    Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.

Additional delivery details

This Dual-Delivery subject has On Campus assessment components.

Last updated: 30 January 2025

Further information

Last updated: 30 January 2025