MTH2015 - Multivariable calculus (advanced) - 2017

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences


Dr Yann Bernard

Unit guides



  • Second semester 2017 (Day)


This unit is an alternative to MTH2010 for students with a strong mathematical foundation.

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. Use of a computer algebra package.


On completion of this unit students will be able to:

  1. Understand and apply multivariable calculus to problems in the mathematical and physical sciences;
  2. Find and classify the extrema of functions of several variables;
  3. Compute Taylor series for functions of several variables;
  4. Compute line, surface and volume integrals in Cartesian, cylindrical and polar coordinates;
  5. Apply the integral theorems of Green, Gauss and Stokes;
  6. Use computer algebra packages to solve mathematical problems;
  7. Present a mathematical argument in written form;
  8. Understand and apply the formal definition of a limit to functions of several variables;
  9. Prove various identities between grad, div and curl;
  10. Develop and present rigorous mathematical proofs.


Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Workload requirements

Three 1-hour lectures, one 1-hour workshop and one 2-hour support class per week

See also Unit timetable information

Chief examiner(s)

This unit applies to the following area(s) of study


A High Distinction in VCE Enhancement Mathematics or MTH1030; a Distinction in MTH1035; or by approval of the Head of School of Mathematical Sciences. In order to enrol in this unit students will need to apply via the Science Student Services officeScience Student Services office (


ENG2005, ENG2091, MTH2010