MA40254: Differential and geometric analysis
Academic Year:  2019/0 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA20219 
Description:  Aims: To develop the theory of continuously differentiable maps in finite dimensions, leading to a proof of a general inverse function theorem, and to introduce the theory of differential forms and its applications. Learning Outcomes: After taking this unit, students should be able to state and prove the principal theorems about the Frechet derivative, differential forms and the inverse function theorem, and apply them to simple examples. Skills: Numeracy T/F, A Problem Solving T/F, A Written Communication F (on problem sheets) Content: Review of the Frechet derivative, continuous differentiability and mean value inequality in finite dimensions, contraction mapping theorem. Inverse and implicit function theorems for continuously differentiable maps, surfaces (submanifolds) defined by equations. Differential forms: wedge product, exterior derivative, product rule, pullbacks and change of variables, closed and exact forms, Poincare lemma. differentiable change of variable in ndimensional integrals and integration of nforms. Further topics and applications which might include: matrix groups, Lagrange multiplier rule for constraints, integration of differential forms over simplicial kchains and/or submanifolds with boundary, Stokes' theorem. 
Programme availability: 
MA40254 is Optional on the following programmes:Department of Computer Science

Notes:
