LMAT1222 - Complex Analysis 1 (second year of bachelor in mathematical sciences) or equivalent course
Reminders of complex analysis, conformal mappings, Möbius transformations, Riemann mapping theorem, asymptotic methods (Laplace method, steepest descent method), special functions
At the end of this learning unit, the student is able to :
Contribution of the course to learning outcomes in the Master in Mathematics programme. By the end of this activity, students will have made progress in: |
- Recognise and understand a basic foundation of mathematics. In particular:
-- Recognise the fundamental concepts of important current mathematical theories.
-- Establish the main connections between these theories.
- Show evidence of abstract thinking and of a critical spirit. In particular:
-- Identify the unifying features of different situations and experiments in mathematics or in closely related fields (probabilty and statistics, physics).
-- Argue within the context of the axiomatic method.
-- Construct and draw up a proof independently, with clarity and rigour.
Learning outcomes specific to the course. By the end of this activity, students will be able to:
(a) Understand and apply the major results from complex analysis.
(b) Understand the theory of conformal mappings and Möbius transformations.
(c) Construct bijective conformal mappings between simple domains.
(d) Understand and use several asymptotic methods.
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the program(s) can be accessed at the end of this sheet, in the section entitled 'Programmes/courses offering this Teaching Unit'.
- J.B. Conway, Functions of one complex variable.
- J.E. Marsden and M.J. Hofman, Basic complex analysis, third edition.