Course overview
This course introduces the fundamental concepts in multivariable calculus. Students will be able to recognise and formulate the equations of paths, surfaces and volumes in three dimensions, compute partial derivatives and the gradient, divergence, curl and Laplacian of given functions, and calculate integrals over paths, surfaces and volumes. They will be able to recall and apply Greens, Stokes and the divergence theorem to appropriate integrals. They will be able to interpret the results of all these calculations in the context of problems from science and engineering.
Course learning outcomes
- Recognise, and be able to formulate, the equations of curves, surfaces and volumes in three dimensions (including in parametric form and in polar coordinates)
- Recall, and be able to calculate, vector derivatives including grad, div, curl and Laplacian (in both Cartesian and orthogonal curvilinear coordinates) and give physical interpretations of these quantities. Be able to write expressions involving vector derivatives using suffix notation and manipulate them to derive identities
- Find, and determine the type of, critical points of multivariable functions, and use Lagrange multipliers to find maxima and minima of functions under constraints
- Calculate integrals over paths, surfaces and volumes (including changing the order of integration, or making changes of variables)
- Recall, and be able to apply Green’s, divergence and Stokes’ theorems when computing integrals
- Apply the theories learned in the course to problems in science and engineering and provide interpretations of the results of these calculations
Degree list
The following degrees include this course