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00:00:00

Hello and welcome to another easy matte video

00:00:02

in this video we are going to calculate the

00:00:05

inverse transform of 1 over s

00:00:07

squared plus s minus 2 to calculate

00:00:10

this inverse transform we have to

00:00:12

separate this fraction into

00:00:15

partial fractions and that way we are going to

00:00:17

calculate the inverse of a very

00:00:19

simple way then we are going to start

00:00:21

by writing the fraction that is 1 over s

00:00:23

squared plus s minus 2 and the first thing to

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do is factor the

00:00:28

denominator in this case we can

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factor it as that plus 2 times s minus 1

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now what we do is to place this

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as two fractions a sum of two

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fractions that will be a constant

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on the first factor which is s plus two

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plus another constant b on the second

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factor which is s minus 1 we have to

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find the value of a and b for that

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what what we are going to do is imagine that

00:00:58

this product is plus 2 times s minus 1

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we pass it to the right side

00:01:02

multiplying here we have it dividing

00:01:04

pass multiplying

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when pass multiplying this s plus 2

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that is going to be multiplying with this s

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plus 2 that is dividing are going to

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cancel and we will be left with the has

00:01:15

multiplied by s minus 1 and when

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multiplying to the second fraction the s

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minus 1 that will be multiplying with

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the s minus 1 that is dividing will be

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canceled and we will only be left with

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lc more 2 multiplying b

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now what we are going to do here is give

00:01:33

values to that we can give the value that

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we want but there are values that

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are more convenient for us, for

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example if that were equal to 1 when

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substituting here we would have 1 minus one

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which is zero and zero times a is zero so

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we eliminate one of the unknowns and

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we are left with only b so

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since that is worth one here we will have 1

00:01:59

+ 2 which is 3 x b because we have 3 b left so

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on the left side we have 1 left

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that we had and on the right side

00:02:06

we only have 3 b left, here this 3

00:02:10

that is multiplying happens by dividing and

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we are then left with a third that is

00:02:13

equal to b and thus we have already obtained the

00:02:16

value of b to obtain the value of a

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we are going to give another value to that which

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is convenient for us now in this case

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we would like to cancel the b for that we

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notice that if s was worth minus two minus

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two plus two it would give us zero and thus we

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cancel the b so we are going to put that

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if s is equal to minus 2

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this part is worth 0 so we are not

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going to write it anymore and here

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- 2 - 1 we are going to have minus 3 now

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because we have minus 3 left

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so we have 1 left and on the

00:02:47

right the minus 3

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now this minus three that is

00:02:51

multiplying and dividing and we are

00:02:54

left with minus one third equal to a and

00:02:57

then we have the value

00:03:05

of both a and how it should. We can substitute them here and we are then left with minus one third over that plus two that this is the value of a and

00:03:08

plus one third over that minus one that

00:03:10

this is the value must then

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we can express this fraction as this

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sum of fractions and as we know the

00:03:19

inverse transform of a sum

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we can separate it into two

00:03:24

inverse transforms we can also extract these constants

00:03:26

from the

00:03:28

inverse transform and write this In the following

00:03:30

way, we take the minus one third, which is a

00:03:32

constant, from the

00:03:34

inverse transform and inside we leave only one

00:03:37

over that plus two and then to that we are going to

00:03:40

add the one third that we also take

00:03:42

from the inverse transform and inside

00:03:45

the transform inversely we are left

00:03:46

with only 1 over that minus 1

00:03:48

now we simply have to calculate these

00:03:51

two inverse transforms and for that

00:03:54

we are going to use the following formula

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the transform of the exponential of ate

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is equal to 1 over s minus a in this

00:04:02

case notice that a is equal to minus 2 in

00:04:06

the first case because if a is worth minus 2

00:04:09

here this minus of the formula with the

00:04:12

minus of 2 is going to be multiplied we will

00:04:16

have more left and then that's how we get that plus 2

00:04:19

so a is worth minus 2 so we

00:04:22

is going to be raised to minus 2 t for

00:04:25

this first case so we are left with

00:04:27

minus one third of raised to minus 2 t and

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for the second case notice that

00:04:33

directly a is equal to 1 so we are going to

00:04:35

have the one raised to 1 t that is raised to

00:04:38

t so it is plus a third of it to the t

00:04:41

and this here is the result of the

00:04:44

inverse transform of this fraction in

00:04:47

this way we can calculate many

00:04:49

inverse transforms simply by

00:04:51

separating into partial fractions I

00:04:53

invite you to calculate the

00:04:54

following inverse transform of the

00:04:56

square by doing the separation into

00:04:58

partial fractions and in the following

00:05:00

video I show you the

00:05:01

complete procedure for what

00:05:03

in your response, if you liked this video,

00:05:05

support me by giving me a like, subscribe

00:05:07

to my channel and share my videos and

00:05:09

remember that if you have any

00:05:11

questions or suggestions you can leave them in

00:05:13

the comments

Description:

📩¿Necesitas ayuda con ejercicios? https://www.facebook.com/unsupportedbrowser 📲 . Anterior: https://www.youtube.com/watch?v=QHql-u6f2ro Siguiente: https://www.youtube.com/watch?v=7Yi67_rwfAQ Ecuaciones Diferenciales Ordinarias EDO: https://www.youtube.com/playlist?list=PL9SnRnlzoyX0RE6_wcrTKaWj8cmQb3uO6 En este video veremos cómo calcular la transformada inversa de Laplace de una fracción, mediante separación en fracciones parciales, paso a paso. __________________________________ ** ENLACES IMPORTANTES ** VIDEOS DE LA FUNCIÓN GAMMA: https://www.youtube.com/playlist?list=PL9SnRnlzoyX0HaV0wt4IXkZCnitRfGhTc LISTA COMPLETA SOBRE TRANSFORMADAS DE LAPLACE: https://www.youtube.com/playlist?list=PL9SnRnlzoyX25JXGxmFgMEnexFeml0zKu Curso de Ecuaciones Diferenciales Ordinarias (EDO): https://www.youtube.com/playlist?list=PL9SnRnlzoyX0RE6_wcrTKaWj8cmQb3uO6 Aplicaciones de las Ecuaciones Diferenciales: https://www.youtube.com/playlist?list=PL9SnRnlzoyX3nM-vp3hPmDvm195QK8NFe Curso de Ecuaciones Diferenciales Parciales (EDP): https://www.youtube.com/playlist?list=PL9SnRnlzoyX05Y-DlDAoD4KwuHeNoP39F Curso de Integrales: https://www.youtube.com/playlist?list=PL9SnRnlzoyX39hvLuyYgFEIdCXFXI3xaU Curso de Derivadas: https://www.youtube.com/playlist?list=PL9SnRnlzoyX1kIbHdA7GN-6g-hvkyLbWp Videos Exclusivos: https://www.youtube.com/playlist?list=UUMOHwtud9tX_26eNKyZVoKfjA Curso de repaso de matemáticas (preuniversitarias) https://www.youtube.com/playlist?list=PL9SnRnlzoyX1-FFtFcUupLSdnTRvs8B5K __________________________________ ** MIRA TODOS MIS CURSOS AQUÍ ** https://docs.google.com/spreadsheets/d/18es27SWnWkWTGE8QCEpwdldRgGyzSvECWVUCmtactv8/edit __________________________________ ** BIBLIOGRAFÍA ** - Ecuaciones Diferenciales, Edwards y Penney - Ecuaciones Diferenciales, Dennis G. Zill - Ecuaciones Diferenciales, Daniel A. Marcus - Ecuaciones Diferenciales, Boyce DiPrima - Ecuaciones Diferenciales, Richard Haberman - Ecuaciones Diferenciales, Nagle - Ecuaciones Diferenciales, Rainville __________________________________ ** DONACIONES ** - Paypal: https://www.paypal.com/donate/ - Membresías del canal: https://www.youtube.com/channel/UCHwtud9tX_26eNKyZVoKfjA/join - Patreon: https://www.patreon.com/matefacil __________________________________ ** MIS OTROS CANALES Y REDES SOCIALES ** - Grupo de Telegram: https://t.me/matefacilgrupo - Canal de Física: https://www.youtube.com/channel/UCeFNpG-n8diSNszUAKaqM_A - Canal de Videojuegos: https://www.youtube.com/channel/UClSpw-rlRdygJmI33x1YagA - Twitch: https://www.twitch.tv/matefacil - Facebook (Página): https://www.facebook.com/unsupportedbrowser - Twitter: https://www.twitter.com/matefacilx - Instagram: https://www.facebook.com/unsupportedbrowser - TikTok: https://www.tiktok.com/@matefacilx - Discord: https://discord.com/invite/Gmb7sF9 __________________________________ #Matefacil #Matematicas #Math #tutorial #tutor #tutoriales #profesor __________________________________

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