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;
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.
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 and at supplementals where applicable.