
Academic Year:  2018/9 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Intermediate (FHEQ level 5) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA20218 
Description:  Aims: To extend the theory of differentiation from functions of one real variable to functions of several real variables and to functions of one complex variable. To understand the relationship between these theories, their geometrical interpretation, and their application through examples. Learning Outcomes: After taking this unit students should be able to: * state definitions and theorems in real and complex analysis and present proofs of the main theorems * construct their own proofs of simple unseen results and of simple propositions * present mathematical arguments in a precise, lucid and grammatical fashion * apply definitions and theorems to simple examples * give a geometric interpretation of multivariate differentiation * evaluate simple contour integrals in the complex plane. Skills: Numeracy T/F A Problem Solving T/F A Spoken and Written Communication F (in tutorials and on problem sheets) Content: Frechet derivative as best linear approximation, partial and directional derivatives. Continuous differentiability, Jacobian matrix, chain rule, higher order partial derivatives, equality of continuous 2nd derivatives. Exterior derivative of a 1form (covector field), divergence and curl of a vector field, Hessian, stationary points and second derivative test, Taylor's theorem. Complex differentiable functions and the CauchyRiemann equations, Curves in C, contour integrals. Primitives, Cauchy's theorem, Cauchy's Integral Formula, representation by power series. Liouville's Theorem, Fundamental Theorem of Algebra. Principal parts, Residue Theorem. 
Programme availability: 
MA20219 is Compulsory on the following programmes:Department of Computer Science
MA20219 is Optional on the following programmes:Department of Economics

Notes:
