Class notes
Variable y Función Compleja
- Course
- Institution
Incluye operaciones elementales de la variable compleja así como la introducción de las funciones complejas.
[Show more]
Seller
Follow
AeroLibrary
Content preview
VARIABLE COMPLETAfk = k
utorno
=> = Bola abierta = B([0.3)=(ECK/120-21 9}
f(z) f(x = + iy) (
=
u+
- iv u(x,y) + iv(x,y)
-
Argumento principal: Oc(M. i]
Ejemplo:
8: D: IRF 8:1 i
DIE 1E1 + Arg(z)
Arglz)
f(z) (t) =
"I
·
·I -
L
-
B ⑱ a
"I'll
condiciones para que una funcion sea funcion:
-
-
Todos los elementos del
Un elemento del conjunto
conjunto departida tienen imagen.
departida solo puede tener una imagen.
B
Hay algunas funciones son multievaluadas, decir funciones los cuales los elementos del dominio le corresponden varias
que es en a
imagenes. - P.e.f(x) x =
En
f(x) =
xhaydosramas, Hay que elegir una rama con la cual trabajar.
LIMITE DE FUNCIONES COMPLEJAS
limf(x-ec.53:5850/1EEK6:18171.1K9 Paracalcular el limite de
estedefinida
una funcion no have falta
que la funcion que
en el punts.
LIMITEENO Eiemplo:
line f(b/z) lim 1. E
1 E
-
E + O E +1
LIMITE INFINITO lim 1-(1 -
(1) 1 lim
5-(+ix) 1
-
j =
x 01 (x + iy)
=
- x1
= 1-(1-iy)
x+1 *
8
lime
+ 8
(f(2) = 0
E
CONTINUIDAD
Yes continua en to si,x9+058%0/12.Cokc8 =
(812) f(colk
limf(x) =
f(20) Esta no
hay que usaat
, EjemplO:
lim
E s
1s.lime 4RzeidreiG"
+a
=
lim
(2 -3i)(2 + 3i)
lim =
6i
=
E + 5i = 3i Ei3i E -
3
DERIVADA DE
f1z)
PREVI8 i
8: IRP: 1R9
of -lim flx+af(x). Derivada can respects a or
unreco
I
La derivabilidad no implica continuidad.
La diferenciabilidad si implica continuidad
dEl)
lf(x h1 f(x)
↓i.
m
+ - -
0
=
1 ill
La funciones diferenciable mando existen (as derivadas parciales, son continuas.
seaf: A -PI ECA
f1)
limf(z
(z)
f'(z)
+
-
=
NZ
=emplo:
f(z) 2 =
(2 -z-
+521
Uz
in
lim
o NZ
Xz + 8
+x
0im-itt
=
I gota
Nz 0x iUY No derivable ningan punto.
dimso
= + es en
inme UN 1
loss =
XX + y WN
Nz Ux-iUY
=
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller AeroLibrary. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $6.35. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
50990 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now