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.
- Functions
- Derivatives
- Integrals
- Fundamental theorems
Course learning outcomes
- Recognise, and be able to formulate how curves, surfaces and volumes in three dimensions can be expressed by equations (including in parametric form and in polar coordinates).
- Recall, and be able to calculate, vector derivatives including gradient, divergence, curl and Laplacian (in both Cartesian and orthogonal curvilinear coordinates) and give physical interpretations of these quantities.
- 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 mathematical concepts of CLOs 1, 2, 3, 4 and 5 to problems arising in other relevant disciplines, and interpret the results.
Degree list
The following degrees include this course