
Academic Year:  2012/3 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 
Level:  Intermediate (FHEQ level 5) 
Period: 
Semester 2 
Assessment:  EX 100% 
Supplementary Assessment:  MA20219 Mandatory extra work (where allowed by programme regulations) 
Requisites:  Before taking this unit you must take MA10207 and take MA10209 and take MA10210 and take MA20218 
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 semiconvex 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 semiconvex domains in R^{3}, Green's theorem, oriented surfaces, Stokes' theorem, geometric interpretation of div, curl and grad, Green's identities. 
Programme availability: 
MA20219 is Compulsory on the following programmes:Department of Computer Science
MA20219 is Optional on the following programmes:Department of Mathematical Sciences
