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Academic Year: | 2013/4 |
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 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. |
Programme availability: |
MA20219 is Compulsory on the following programmes:Department of Computer Science
MA20219 is Optional on the following programmes:Department of Mathematical Sciences
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