On successful completion of this module, students will be able to:

Manipulate vectors in R^3 to evaluate dot products and cross products and investigate if vectors are linearly independent;

Understand the concepts of vector fields, conservative vector fields, curves and surfaces in R^3;

Find the equation of normal lines and tangent planes to surfaces in R^3;

Evaluate line integrals and surface integrals from the definitions;

Use Green's Theorem to evaluate line integrals in the plane and use the Divergence Theorem (Gauss's Theorem) to evaluate surface integrals;

Apply Stokes's Theorem to evaluate line integrals and surface integrals;

Solve first order PDEs using the method of characteristics and solve second order PDEs using separation of variables;

Module Content

Vector algebra in R^3. Vector fields, curves and surfaces in R^3.

Theorems of Green, Stokes and Gauss.

PDEs of first and second order

Module Prerequisite

MAU22S01

Assessment Detail

This module will be examined in a 2 hour examination in Trinity term.Continuous assessment will contribute 20% to the final grade for the module at the annual
examination session.