Calculus of Several Variables (G5141)

15 credits, Level 5

Autumn teaching

  • Functions of several variables. Limits, continuity.
  • Differentiation of functions of several variables. Directional derivatives, gradient, total and partial differentials. Taylor formula.
  • Extrema, constrained minima and maxima. Lagrange multipliers.
  • Implicit Function Theorem.
  • Double and Triple integrals. Polar, cylindrical and spherical coordinates.
  • Line and surface integral. Gauss and Stokes Theorem.


61%: Lecture
19%: Practical (Workshop)
20%: Seminar


20%: Coursework (Portfolio, Problem set)
80%: Examination (Unseen examination)

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 39 hours of contact time and about 111 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2021/22. However, there may be changes to these modules in response to COVID-19, staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of material changes to modules at the earliest opportunity.