MTH2010 - Multivariable calculus - 2019

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

Chief examiner(s)

Associate Professor Todd Oliynyk


Associate Professor Todd Oliynyk (Semester 1)
Dr Yann Bernard (Semester 2)

Unit guides



  • First semester 2019 (On-campus)
  • Second semester 2019 (On-campus)


MTH1030, MTH1035, or MTH1085


ENG2005, ENG2091, MTH2015


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 spherical 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.


NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

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

Workload requirements

Three 1-hour lectures and one 2-hour applied class per week

See also Unit timetable information

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