Short Description
This course aims to develop topics in multivariable calculus. It is an essential course for intending honours students. The emphasis in on methods and applications.

Assessment
One degree examination (80%) (1 hour 30 mins); coursework (20%).
Main Assessment In: December

Course Aims
This course aims to develop topics in multivariable calculus. It is an essential course for intending honours students. The emphasis in on methods and applications.
Intended Learning Outcomes of Course
By the end of the course, students should have attained the following learning objectives:

- Partial differentiation: Drawing three dimensional surfaces using cross-sections and contours; definition of a partial derivative; the chain rule for partial derivatives;
- solving simple PDEs by using a given change of variable.
- Differential vector calculus: Parametrisation of curves in two and three dimensions; scalar and vector fields; definitions of div, grad and curl; identities involving these derivatives; potentials and conservative vector fields.
- Double and triple integration: Volume under a surface and double integration; obtaining limits for a given domain; change of order of integration; change to polar coordinates and the area element; interpretation of triple integral; spherical polar coordinates; general change of variables and the Jacobian.
- Line and surface integrals: Definitions of arc length and line integral; conservative vector fields and path-independence of line integrals; parametric description of a surface; definition of a surface integral; use of polar coordinates.
- Green's theorem and the divergence theorem: Comparison between the fundamental theorem of calculus, Green's theorem and the divergence theorem; applications of Green's theorem to evaluating closed line integrals; applications of the divergence theorem to evaluating closed surface integrals.
- Be able to learn and apply formulae used in this course.

*Course content subject to change