Variable Complexa

Bibliografia útil

Webs útils

Complex Analysis

An online interactive introduction to the study of complex analysis.

https://complex-analysis.com/content/table_of_contents.html

Complex Analysis - A Visual and Interactive Introduction (Ponce Campuzano)

The study of complex analysis is important for students in engineering and the physical sciences and is a central subject in mathematics. In addition to being mathematically elegant, complex analysis …

https://math.libretexts.org/Bookshelves/Analysis/Complex_Analysis_-_A_Visual_and_Interactive_Introduction_(Ponce_Campuzano)

Playlists útils

Engineering Math: Crash Course in Complex Analysis

This series provides a high level overview of complex analysis needed to understand differential equations. This is meant to be about a two week course. I as...

https://www.youtube.com/playlist?list=PLMrJAkhIeNNQBRslPb7I0yTnES981R8Cg

Analysis of a Complex Kind

This playlist contains the videos of the Coursera MOOC "Analysis of a Complex Kind" by Petra Bonfert-Taylor. Copyright Wesleyan University.

https://youtube.com/playlist?list=PLi7yHjesblV0sSfZzWdSUXGO683n_nJdQ

Graficar Funcions (plotters)

Complex Function Plotter

Smooth, responsive visualization tool for complex functions parameterized by an arbitrary number of variables.

https://samuelj.li/complex-function-plotter/#z-t

Complex Function Viewer

IdentitySquareCubeCardiodSinCosExpInvertPoissonConvexKoebeAirfoil zz2z3z + (1/2)z2sin zcos zez1/z(1+z)/(1-z)z/(1-z)z/(1-z)2z + 1/z

http://www.falstad.com/complexviewer/

Vídeo molt xulo (formal i amb visualitzacions)

Fotografies xules

Com visualitzar funcions complexes

Introducció

• A nivell intuïtiu: Playlist de Mathemaniac per entendre-ho viusalment

• A nivell tècnic: Vídeos de MathsUp i vídeos de la playlist de TheMathCoach.

Operacions amb números complexes (a partir del minut 13)

Diferenciabilitat, Cauchy-Riemann, Funcions analítiques:

Tipus de Singularitats:

Què polles és una determinació?

Entendre realment com les superfícies de Riemann representen funcions multivaluades

Teorema del residu, demostració "visual" (40 min):

Integral Pac-Man explicada perfecte:

Triar bé quin mètode d'integració aplicar:

Extra

Mapa mental de la base matemàtica: