MATH201-23S1 (C) Semester One 2023

Multivariable Calculus

15 points

Start Date: Monday, 20 February 2023
End Date: Sunday, 25 June 2023
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 5 March 2023
  • Without academic penalty (including no fee refund): Sunday, 14 May 2023


This course deals with techniques in multivariable calculus and vector calculus which have applications in many areas of science, commerce and engineering. It is also preparation for many courses in advanced mathematics.

This course covers techniques in multivariable calculus and vector calculus and interesting applications in many areas of science, commerce and engineering. It is useful for all Math majors, and for students who want to proceed to study more advanced topics in mathematics.

Topics covered: geometry of multivariable functions, partial derivatives, linearisation, multivariate chain rule, implicit function theorem; multivariate optimisation, sufficient conditions for optimality, Lagrange multipliers for optimisation problems; iterated integrals, polar coordinates; Jacobian determinants; parametric curves, tangent vectors, line integrals, work integrals; div, grad, curl; surface integrals; volume integrals; Green's Theorem; Stokes Theorem; Divergence Theorem; physical applications.

Learning Outcomes

  • Students successfully completing this course should:
  • be proficient in the basic techniques of multivariable calculus.
  • be able to use calculus methods to solve standard applied problems and to apply their understanding of multivariate geometry to express and solve vector calculus problems.
  • Have developed problem solving skills both as part of a team and as an individual.



MATH261, MATH264, EMTH202, EMTH204, EMTH210

Course Coordinator

Felipe Voloch


Michael Plank


Assessment Due Date Percentage 
Homework assignments 25%
Test 25%
Final examination 50%

Textbooks / Resources

Recommended Reading

Stewart, James; Calculus : early transcendentals ; Eighth edition; Cengage Learning, 2016 (Earlier editions of the text are also suitable).

Indicative Fees

Domestic fee $824.00

International fee $4,750.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH201 Occurrences

  • MATH201-23S1 (D) Semester One 2023 (Distance) - Not Offered - see department for alternatives
  • MATH201-23S1 (C) Semester One 2023