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UnitLevel 2Undergraduate

MTH2010 Multivariable calculus

Faculty of Science

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MTH2010 Multivariable calculus is a level 2, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2025 in Semester 1 and Semester 2 at Clayton. It has no prerequisites and unlocks 28 units, leading on to 77 units in all.

Credit points
6
Offered in 2025
Semester 1, Semester 2
Clayton
Assessment
Exam 50%
and 1 other task

This is the 2025 handbook entry. See the 2027 entry.

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Requisites

Before MTH2010

No prerequisites or corequisites besides the enrolment rules below.

After MTH2010

28 units list MTH2010 as a prerequisite or corequisite.

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Enrolment rules

PROHIBITION: ENG2005, MTH2015, MTH2019 and incompatible with course versions E3001, E3002, E3003, E3004, E3005, E3006, E3007, E3008, E3009, E3010, E3011, L3002.

PREREQUISITE: You must have passed MTH1030, MTH1035, or MTH1040

Equivalent units

The same content under another code. Only one of them counts.

Overview

Functions of several variables, partial derivatives, extreme values, Lagrange multipliers. Multiple integrals, line integrals, surface integrals. Vector differential calculus; grad, div and curl. Integral theorems of Gauss and Stokes. 

Offerings in 2025

Teaching periodCampusMode
First semesterClaytonOn campus
Second semesterClaytonOn campus

Assessment

  • Continuous assessmentDemonstration
    50%
  • Final assessment - Exam (3 hours and 10 minutes)Examination
    50%

Learning outcomes

When you finish this unit, you should be able to:

  1. 1

    Apply multivariable calculus to problems in the mathematical and physical sciences;

  2. 2

    Find and classify the extrema of functions of several variables;

  3. 3

    Compute line, surface and volume integrals in Cartesian, cylindrical and spherical polar coordinates;

  4. 4

    Apply the integral theorems of Green, Gauss and Stokes;

  5. 5

    Present a mathematical argument in written form.

Workload and teaching

  • Seminars36 hours
  • Applied sessions22 hours
  • Teaching approachActive learning
  • Three 1-hour seminars;
  • One 2-hour applied class (in weeks 2-12) and
  • 7 hours of independent study per week.

Active learning will occur in lectures and applied classes.

Learning resources

Required resources

Calculus, Metric Version by James Stewart, Cengage Learning, 9th edition, or individual chapters.

Where it fits

MTH2010 is part of 17 areas of study in the 2025 handbook.

Contacts

Unit Coordinators
Dr Julie Clutterbuck
Professor Todd Oliynyk
Chief Examiners
Professor Todd Oliynyk

Common questions

What are the prerequisites for MTH2010?

MTH2010 has no prerequisites, but enrolment rules apply.

What can I take after MTH2010?

MTH2010 is a prerequisite or corequisite for 28 units, including ASP2062, ASP3012, ASP3051, ASP3162, CHE3162 and CHE3167. Those lead on to 77 units in all.

When is MTH2010 offered?

In 2025, MTH2010 runs in Semester 1 and Semester 2 at Clayton.

Does MTH2010 have an exam?

Yes. The exam is worth 50% of the final mark, alongside 1 other task.

Which majors and minors include MTH2010?

MTH2010 is part of Applied mathematics; Astrophysics; Atmospheric science; Financial and insurance mathematics; and Mathematical statistics, and 3 other areas of study.

More details

Credit points
6
Level
2
Study level
Undergraduate
Faculty
Faculty of Science
Organisational unit
School of Mathematics
Type
Coursework
EFTSL
0.125
Student contribution
SCA Band 1
Study abroad
Available
Handbook years
20202021202220232024202520262027