Department of Mathematical Sciences, Unit Catalogue 2010/11 |
MA20219: Analysis 2B |
 Credits:
| 6 |
| Level:
| Intermediate |
| Period: | This unit is available in... |
| Semester 2 |
| Assessment:
| EX100 |
| Supplementary Assessment: | Supplementary assessment information not currently available (this will be added shortly) |
| Requisites:
| Before taking this unit you must take MA10207 and take MA10209 and take MA10210 and take MA20218 or equivalent units from MA10001 - MA10006. |
| Description:
| Aims: To complete the rigorous theory of elementary multivariate calculus begun in Analysis 2A. To illustrate the geometrical meaning and potential applications of the main results through examples. Learning Outcomes: After taking this unit, students should be able to: * state definitions and theorems in real analysis and present proofs of the main theorems * construct their own proofs of simple unseen results and construct proofs of simple propositions * Present mathematical arguments in a precise, lucid and grammatical fashion. * Apply definitions and theorems to simple examples. * Apply mathematics rigorously to problems from geometry and physics. * Give a geometrical and physical interpretation of multivariate calculus. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials). Content: Vector fields: div, curl, grad. Del operator, second order derivatives. Line integrals: arc length, work integrals, conservative vector fields; criteria for the existence of a potential. Multiple Riemann integration: criteria for integrability, exchanging the order of integration (Fubini), volume integrals for semi-convex domains, statement (without proof) of the change of variables formula, Cartesian, polar and cylindrical coordinates for the change of variables formula. Parametrised surfaces: surface area, surface integrals, change of variables for surface integrals, surface integrals independent of parametrisation. Divergence theorem for semi-convex domains in R3, Green's theorem, oriented surfaces, Stokes' theorem, geometric interpretation of div, curl and grad, Green's identities. |