Complex analysis#

Table of contents#

  1. Introduction

  2. Complex plane

  3. Complex functions

  4. Holomorphic functions

  5. Complex integration

  6. Fractals

Further reading and references#

  • Prof Velisa Vesovic’s lecture notes on Maths Methods 2 (available internally on ESESIS)

  • Elias Wegert’s book Visual Complex Functions

  • Dr Sheehan Olver’s lecture notes on Applied Complex Analysis and his Julia script ComplexPhasePortrait.jl motivated many visualisations and our Python implementation of them

  • Ablowitz, M.J., Fokas, A.S. and Fokas, A.S., 2003. Complex variables: introduction and applications. Cambridge University Press.

  • Arfken, G.B. and Weber, H.J., 1999. Mathematical methods for physicists.

  • Ruban, A.I. and Gajjar, J.S., 2014. Fluid Dynamics: Classical Fluid Dynamics. Oxford University Press, USA.