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Funciones de variable compleja.pptx
1. Funciones de una variable
compleja
Francisco Rafael Arreguín Correa
Materia
2. En una función de variable real y=f(x) a la abscisa x le
corresponde la ordenada y. Una gráfica de la
función y=f(x) en el intervalo a<x<b está definida por el
conjunto de puntos (x,f(x)) del plano.
Sin embargo, w=f(z) es una función de variable compleja.
A cada punto del plano z=x+iy le corresponde un punto
del plano w=u+iv
9. En una función de variable real y=f(x) a la abscisa x le correponde la ordenada y. Una gráfica de la
función y=f(x) en el intervalo a<x<b está definida por el conjunto de puntos (x,f(x)) del plano.
Sin embargo, w=f(z) es una función de variable compleja. A cada punto del plano z=x+iy le corresponde
un punto del plano w=u+iv
Func
10. The slide title goes here!
Do you know what helps you make your point clear?
Lists like this one:
● They’re simple
● You can organize your ideas clearly
● You’ll never forget to buy milk!
And the most important thing: the audience won’t miss the point
of your presentation
11. Whoa
This can be the part of the presentation where you
introduce yourself, write your email…
12. 01 02 03
Transformaciones lineales
Son funciones entre K-espacios vectoriales que son compatibles
con la estructura (es decir, con la operación y la acción) de estos
espacios.
13. 01 02 03
Transformaciones lineales
Son funciones entre K-espacios vectoriales que son compatibles
con la estructura (es decir, con la operación y la acción) de estos
espacios.
16. Transformaciones
lineales
You can give a brief description of the topic you
want to talk about here. For example, if you want to
talk about Mercury, you can say that it’s the
smallest planet in the entire Solar System
17. Transformaciones
lineales
You can give a brief description of the topic you
want to talk about here. For example, if you want to
talk about Mercury, you can say that it’s the
smallest planet in the entire Solar System
18. Transformaciones
lineales
You can give a brief description of the topic you
want to talk about here. For example, if you want to
talk about Mercury, you can say that it’s the
smallest planet in the entire Solar System
19. —Someone Famous
“This is a quote, words full of wisdom
that someone important said and can
make the reader get inspired.”
20. —Someone Famous
“This is a quote, words full of wisdom
that someone important said and can
make the reader get inspired.”
21. Mercury Venus
Venus has a beautiful name and
is the second planet from the Sun.
It’s hot and has a poisonous
atmosphere
Mercury is the closest planet to
the Sun and the smallest one in
the Solar System—it’s only a bit
larger than the Moon
Combined operations
23. Mercury
It’s the closest planet to the
Sun and the smallest in the
Solar System
Venus
Venus has a beautiful
name and is the second
planet from the Sun
Mars
Despite being red, Mars is
actually a cold place. It’s
full of iron oxide dust
Multiplication of numbers
24. 9h 55m 23s
Jupiter's rotation period
333,000.000
The Sun’s mass compared to Earth’s
386,000 km
Distance between Earth and the Moon
25. Venus
Venus is the second
planet from the Sun
Jupiter
It’s the biggest planet
in the Solar System
Mars
Despite being red,
Mars is a cold place
Saturn
Saturn is a gas giant
and has several rings
Dividing numbers
27. Mercury
It’s the smallest planet of
them all
Venus
Venus is the second
planet from the Sun
Jupiter
Jupiter is the biggest
planet of them all
Saturn
It’s composed of
hydrogen and helium
Mars
Mars is actually a very
cold place
Neptune
It’s the farthest planet
from the Sun
Algebraic expressions
28. Algebraic operations
Venus
Venus is the second
planet from the Sun
Jupiter
Jupiter is the biggest
planet of them all
Mars
Despite being red,
Mars is a cold place
Saturn
Saturn is a gas giant
and has several rings
29. A picture always
reinforces the
concept
Images reveal large amounts of data, so
remember: use an image instead of a long text.
Your audience will appreciate it
30. A picture always
reinforces the
concept
Images reveal large amounts of data, so
remember: use an image instead of a long text.
Your audience will appreciate it
31. A picture always
reinforces the
concept
Images reveal large amounts of data, so
remember: use an image instead of a long text.
Your audience will appreciate it
32. A picture always
reinforces the
concept
Images reveal large amounts of data, so
remember: use an image instead of a long text.
Your audience will appreciate it
33. This is a map
Latin America
Venus has a beautiful name
and is the second planet from
the Sun
Europe
Despite being red, Mars is
actually a cold place. It’s full
of iron oxide dust
35. Equations: approach
Mercury
Jupiter
Saturn
Venus
Equations
Mercury is the closest planet to the
Sun and the smallest one in the
Solar System—it’s only a bit larger
than the Moon
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here
36. Steps to tackle equations
01
Read
problem
Venus is the
second planet
from the Sun
02
Identify
unknown
Jupiter is the
biggest planet of
them all
03
Approach
equation
Despite being red,
Mars is a cold
place
04
Solve
equation
Saturn is a gas
giant and has
several rings
05
Answer
question
Mercury is the
smallest planet of
them all
37. X - 5 = 3
Example of an equation
Unknown
Jupiter is the biggest planet
of them all
First member
Saturn is composed of
hydrogen and helium
Second member
Neptune is very far away
from Earth
39. Activities
● A number increased by 8 equals 22. What number is it? --
● Maria's age increased by 7 equals 15. How old is Maria? --
● Double a number equals 46. Find that number --
● If half of Marta's age is equal to 10, how old is Marta? --
● The triple of a number decreased by 1 is equal to 20. Find that number --
40. Solve the problem
Saturn is a gas giant and has several
rings. It's composed mostly of hydrogen
and helium. It was named after the Roman
god of wealth and agriculture
Problem Solution
--
41. Do these exercises
Solve: Result
7 x 4 --
6 x 8 --
3 x 9 --
5 x 5 --
4 x 8 --
Solve: Result
3 x 6 --
2 x 8 --
9 x 2 --
7 x 9 --
2 x 6 --
42. Practical exercise
Exercise A
Venus has a beautiful
name and is the second
planet from the Sun
Exercise B
Despite being red, Mars is
actually a cold place. It’s
full of iron oxide dust
Result
--
Result
--
43. Interpretation exercise
Interpret a multiplication equation as a comparison, for example:
35 = 5 × 7
35 is 5 times as
many as 7
7 times as many as
5
Comparison A
Despite being red, Mars is a
very cold place
Comparison B
Saturn is a gas giant and
has several rings
Interpret
Neptune is the farthest
planet from the Sun
44. Multiples
Observe and match:
Multiples of 5
Multiples of 9
Multiples of 6
Multiples of 8
Multiples of 7
Multiples of 4
12, 18, 24, 30
16, 24, 32, 40
15, 20, 25, 30
18, 27, 36,45
14, 28, 35, 42
28, 36, 40, 44
45. Important concepts
Factors
Jupiter is the biggest
planet of them all
Hexagons
Saturn is a gas giant
and has several rings
Equality
Neptune is very far
away from us
Logarithm
Ceres is located in the
asteroid belt
Binomial
Mercury is the
smallest planet
Cube
Venus is the second
planet from the Sun
Digit
Mars is actually a very
cold place
Exponent
Earth is the planet
where we live on
47. Tablet
app
You can replace the image on
the screen with your own work.
Just right-click on it and select
“Replace image”
48. Mobile
app
You can replace the image on the
screen with your own work. Just
right-click on it and select “Replace
image”
49. Susan Bones Timmy Jimmy
You can talk a bit about this
person here
You can talk a bit about this
person here
Our team
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