Laplace transform for solving differential equations [closed]
$begingroup$
I am confused about Laplace transform. the only thing that is important in Laplace theorem is the value of $f(t)$ in $t geq 0$.
laplace transform:
$mathcal{L}{f(t)}$ $=$ $int_0^infty ! e^{-st}f(t)$
so as we see in the above transform $f(t)$ if $t<0$ is not important at all. so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
ordinary-differential-equations laplace-transform
asked Jan 11 at 10:05
jack.mathjack.math
616
$endgroup$
closed as unclear what you're asking by Kavi Rama Murthy, Cesareo, metamorphy, amWhy, A. Pongrácz Jan 11 at 14:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I am confused about Laplace transform. the only thing that is important in Laplace theorem is the value of $f(t)$ in $t geq 0$.
laplace transform:
$mathcal{L}{f(t)}$ $=$ $int_0^infty ! e^{-st}f(t)$
so as we see in the above transform $f(t)$ if $t<0$ is not important at all. so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
ordinary-differential-equations laplace-transform
asked Jan 11 at 10:05
jack.mathjack.math
616
$endgroup$
closed as unclear what you're asking by Kavi Rama Murthy, Cesareo, metamorphy, amWhy, A. Pongrácz Jan 11 at 14:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I am confused about Laplace transform. the only thing that is important in Laplace theorem is the value of $f(t)$ in $t geq 0$.
laplace transform:
$mathcal{L}{f(t)}$ $=$ $int_0^infty ! e^{-st}f(t)$
so as we see in the above transform $f(t)$ if $t<0$ is not important at all. so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
ordinary-differential-equations laplace-transform
asked Jan 11 at 10:05
jack.mathjack.math
616
$endgroup$
I am confused about Laplace transform. the only thing that is important in Laplace theorem is the value of $f(t)$ in $t geq 0$.
laplace transform:
$mathcal{L}{f(t)}$ $=$ $int_0^infty ! e^{-st}f(t)$
so as we see in the above transform $f(t)$ if $t<0$ is not important at all. so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
ordinary-differential-equations laplace-transform
ordinary-differential-equations laplace-transform
asked Jan 11 at 10:05
jack.mathjack.math
616
asked Jan 11 at 10:05
jack.mathjack.math
616
asked Jan 11 at 10:05
jack.mathjack.math
616
asked Jan 11 at 10:05
jack.mathjack.math
616
asked Jan 11 at 10:05
jack.mathjack.math
616
616
closed as unclear what you're asking by Kavi Rama Murthy, Cesareo, metamorphy, amWhy, A. Pongrácz Jan 11 at 14:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Kavi Rama Murthy, Cesareo, metamorphy, amWhy, A. Pongrácz Jan 11 at 14:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
In your setting, yes you will find your transform for $t geq 0$.
If you're interested in $mathbb{R}$ you do $$ F(s) = int_{-infty}^infty e^{-st} f(t)$$ which is also known as Bilateral (2-sided) Laplace transform.
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
$endgroup$
$begingroup$
so you say that Laplace transform gives the answer for $t>0$ but I have seen that it is used for $R$. is there a condition so that the answer from Laplace transform is correct in $R$
$endgroup$
– jack.math
Jan 11 at 10:13
$begingroup$
what do you exactly mean by "the answer from Laplace" ???? That does not make any sense. I tried to answer your question to the closest logical question possible.
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:17
$begingroup$
we apply Laplace transform to an equation and find an answer. the phrase "the answer from Laplace" means this answer
$endgroup$
– jack.math
Jan 11 at 10:25
$begingroup$
so once you solve a diff. eqn using Laplace you obtain the answer in Laplace domain .. and then you apply Laplace inverse to go back to time domain. Do you mean that answer ?
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:27
$begingroup$
exactly. you got the point
$endgroup$
– jack.math
Jan 11 at 10:30
|
show 3 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
In your setting, yes you will find your transform for $t geq 0$.
If you're interested in $mathbb{R}$ you do $$ F(s) = int_{-infty}^infty e^{-st} f(t)$$ which is also known as Bilateral (2-sided) Laplace transform.
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
$endgroup$
$begingroup$
so you say that Laplace transform gives the answer for $t>0$ but I have seen that it is used for $R$. is there a condition so that the answer from Laplace transform is correct in $R$
$endgroup$
– jack.math
Jan 11 at 10:13
$begingroup$
what do you exactly mean by "the answer from Laplace" ???? That does not make any sense. I tried to answer your question to the closest logical question possible.
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:17
$begingroup$
we apply Laplace transform to an equation and find an answer. the phrase "the answer from Laplace" means this answer
$endgroup$
– jack.math
Jan 11 at 10:25
$begingroup$
so once you solve a diff. eqn using Laplace you obtain the answer in Laplace domain .. and then you apply Laplace inverse to go back to time domain. Do you mean that answer ?
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:27
$begingroup$
exactly. you got the point
$endgroup$
– jack.math
Jan 11 at 10:30
|
show 3 more comments
$begingroup$
so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
In your setting, yes you will find your transform for $t geq 0$.
If you're interested in $mathbb{R}$ you do $$ F(s) = int_{-infty}^infty e^{-st} f(t)$$ which is also known as Bilateral (2-sided) Laplace transform.
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
$endgroup$
$begingroup$
so you say that Laplace transform gives the answer for $t>0$ but I have seen that it is used for $R$. is there a condition so that the answer from Laplace transform is correct in $R$
$endgroup$
– jack.math
Jan 11 at 10:13
$begingroup$
what do you exactly mean by "the answer from Laplace" ???? That does not make any sense. I tried to answer your question to the closest logical question possible.
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:17
$begingroup$
we apply Laplace transform to an equation and find an answer. the phrase "the answer from Laplace" means this answer
$endgroup$
– jack.math
Jan 11 at 10:25
$begingroup$
so once you solve a diff. eqn using Laplace you obtain the answer in Laplace domain .. and then you apply Laplace inverse to go back to time domain. Do you mean that answer ?
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:27
$begingroup$
exactly. you got the point
$endgroup$
– jack.math
Jan 11 at 10:30
|
show 3 more comments
$begingroup$
so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
In your setting, yes you will find your transform for $t geq 0$.
If you're interested in $mathbb{R}$ you do $$ F(s) = int_{-infty}^infty e^{-st} f(t)$$ which is also known as Bilateral (2-sided) Laplace transform.
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
$endgroup$
so do we find the answer for only $t > 0$ or the answer is correct in $mathbb{R}$?
In your setting, yes you will find your transform for $t geq 0$.
If you're interested in $mathbb{R}$ you do $$ F(s) = int_{-infty}^infty e^{-st} f(t)$$ which is also known as Bilateral (2-sided) Laplace transform.
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
edited Jan 11 at 10:13
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
answered Jan 11 at 10:07
Ahmad BazziAhmad Bazzi
8,0362724
8,0362724
$begingroup$
so you say that Laplace transform gives the answer for $t>0$ but I have seen that it is used for $R$. is there a condition so that the answer from Laplace transform is correct in $R$
$endgroup$
– jack.math
Jan 11 at 10:13
$begingroup$
what do you exactly mean by "the answer from Laplace" ???? That does not make any sense. I tried to answer your question to the closest logical question possible.
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:17
$begingroup$
we apply Laplace transform to an equation and find an answer. the phrase "the answer from Laplace" means this answer
$endgroup$
– jack.math
Jan 11 at 10:25
$begingroup$
so once you solve a diff. eqn using Laplace you obtain the answer in Laplace domain .. and then you apply Laplace inverse to go back to time domain. Do you mean that answer ?
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:27
$begingroup$
exactly. you got the point
$endgroup$
– jack.math
Jan 11 at 10:30
|
show 3 more comments
$begingroup$
so you say that Laplace transform gives the answer for $t>0$ but I have seen that it is used for $R$. is there a condition so that the answer from Laplace transform is correct in $R$
$endgroup$
– jack.math
Jan 11 at 10:13
$begingroup$
what do you exactly mean by "the answer from Laplace" ???? That does not make any sense. I tried to answer your question to the closest logical question possible.
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:17
$begingroup$
we apply Laplace transform to an equation and find an answer. the phrase "the answer from Laplace" means this answer
$endgroup$
– jack.math
Jan 11 at 10:25
$begingroup$
so once you solve a diff. eqn using Laplace you obtain the answer in Laplace domain .. and then you apply Laplace inverse to go back to time domain. Do you mean that answer ?
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:27
$begingroup$
exactly. you got the point
$endgroup$
– jack.math
Jan 11 at 10:30
$begingroup$
so you say that Laplace transform gives the answer for $t>0$ but I have seen that it is used for $R$. is there a condition so that the answer from Laplace transform is correct in $R$
$endgroup$
– jack.math
Jan 11 at 10:13
$begingroup$
so you say that Laplace transform gives the answer for $t>0$ but I have seen that it is used for $R$. is there a condition so that the answer from Laplace transform is correct in $R$
$endgroup$
– jack.math
Jan 11 at 10:13
$begingroup$
what do you exactly mean by "the answer from Laplace" ???? That does not make any sense. I tried to answer your question to the closest logical question possible.
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:17
$begingroup$
what do you exactly mean by "the answer from Laplace" ???? That does not make any sense. I tried to answer your question to the closest logical question possible.
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:17
$begingroup$
we apply Laplace transform to an equation and find an answer. the phrase "the answer from Laplace" means this answer
$endgroup$
– jack.math
Jan 11 at 10:25
$begingroup$
we apply Laplace transform to an equation and find an answer. the phrase "the answer from Laplace" means this answer
$endgroup$
– jack.math
Jan 11 at 10:25
$begingroup$
so once you solve a diff. eqn using Laplace you obtain the answer in Laplace domain .. and then you apply Laplace inverse to go back to time domain. Do you mean that answer ?
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:27
$begingroup$
so once you solve a diff. eqn using Laplace you obtain the answer in Laplace domain .. and then you apply Laplace inverse to go back to time domain. Do you mean that answer ?
$endgroup$
– Ahmad Bazzi
Jan 11 at 10:27
$begingroup$
exactly. you got the point
$endgroup$
– jack.math
Jan 11 at 10:30
$begingroup$
exactly. you got the point
$endgroup$
– jack.math
Jan 11 at 10:30
|
show 3 more comments
