Laplace Transform Ultimate Study Guide
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- Опубликовано: 1 авг 2024
- Laplace Transform Ultimate Study Guide. This includes the Laplace transform of derivatives, Laplace transform of e^(at), Laplace transform of t^n, Laplace transform of sin(bt) & cost(bt), and Laplace transform of hyperbolic functions. We will also talk about the Laplace transform properties such as the shift theorem or the convolution theorem. Some special Laplace transforms will be included such as the Laplace transform of the unit step function, Laplace transform of the Dirac Delta function, Laplace transform of sin(t)/t, Laplace transform of the first and second derivative of the function, Laplace transform of ln(t), and more.
Inverse Laplace Marathon: 👉 • Ultimate Inverse Lapla...
Laplace for you t-shirt: 👉amzn.to/3MV933x
File: 👉 / files-to-laplace-95154820
0:00 start
Q1, Laplace Transform of e^(at), 1:16,
Q2, Laplace Transform of t^n, 6:14,
Q3, Q4, Laplace Transform of sin(bt) & cost(bt), 17:51,
Q5, Laplace Transform of sinh(bt), 24:05,
Q6, Laplace Transform of cosh(bt), 28:33,
Q7, Laplace Transform of the unit step function U(t-a), 32:00,
Q8, Laplace Transform of Window function, 39:05,
Q9, Laplace Transform of Dirac Delta function, 43:56,
Q10, Laplace Transform of f(t-a)u(t-a) and f(t)u(t-a), 51:58,
Q11, Laplace Transform of (t-2)^2*u(t-2) and t^2*u(t-2), 1:04:17,
Q12, Laplace Transform of f(at), 1:09:43,
Q13, Laplace Transform of e^(at)*f(t), 1:19:26,
Q14, Laplace Transform of t^3*e^(2t), 1:23:05,
Q14*, Laplace Transform of e^(3t)*cos(2t), 1:25:58,
Q15, Laplace Transform of t*f(t), 1:28:29, ft. Feynman’s trick, Leibniz rule, differentiation under the integral sign
Q16, Laplace Transform of t*sin(bt), 1:35:45
Extension: Laplace Transform of t^n*f(t), 1:38:19
Q14 again, 1:41:06
Q17, Laplace Transform of f(t)/t, 1:45:55
Q18, Laplace Transform of sin(t)/t, 2:01:30
Honorable mentions: 2:04:03, integral of sin(t)/t from 0 to inf, integral of e^(-t)sin(t)/t from 0 to inf, integral of sin(e^x) from -inf to inf
Q19, Laplace Transform of f'(t), 2:10:33
Q20, Laplace Transform of f''(t), 2:16:26
Q21, Laplace Transform of integral of f(v), 2:22:25
Q22, Convolution theorem, 2:28:11,
**a small mistake in the video: [thanks to Franscious Cummings] 2:35:16 U(t-v). t is the number and v is the variable
Honorable mentions, Laplace Transform of sin(t)cos(t) vs sin(t)*cos(t), 2:44:05
Q23, Laplace Transform of sqrt(t), 2:46:40,
Gamma & Pi functions: • extending the factoria...
(1/2)! = sqrt(pi)/2, • what is half factorial...
Q24, Laplace Transform of ln(t), 2:53:59,
Dr. P: integral of e^(-x)*ln(x) from 0 to inf, • Integral of e^-x ln(x)...
Mu Prime Math: Why Laplace transform can solve differential equations: • 6: Laplace Transforms ...
Chester: Generalized Dirichlet Integral, • Video
Inverse Laplace Transforms Ultimate Study Guide: ruclips.net/video/Gx6yQcmLuH8/видео.html
I fell asleep watching RUclips and woke up 2 hours and 40 minutes into this video… the most confusing way I’ve ever been woken up in my entire life.
Now your subconscious knows the laplace transformation
they are the codes for a nuclear bomb.
When you have nothing to do during the lockdown.
Normal people:-I'm So Boreeeedddd.....
BPRP:-Laplace Transform Marathon GO GO GO!!!!
Nilay Marathe I'm doing integrals instead of laplace transforms
Blackpenredpen yay convolution product
ruclips.net/video/6VGbWFl9kqQ/видео.html
My whole family has coronavirus me and my mother are fine for now my father had the lighter symptoms of the virus and furtunately he feels well now. Greetings from Italy
Ps you really mastered the double pen technique it's almost not visible to the human eye when you switch pens
Stay safe
My whole family is forced to stay home until the first week of april
I am glad to hear that you are all doing okay now. Let me send you and your family my best wishes. We can all overcome this hard time! Stay healthy and stay strong. If there’s anything that you think I can do to help, feel free to let me know.
@@blackpenredpen thank you very much you are a really kind person. What you are doing now by producing content for us is enough to make this whole nightmare lighter. We have a really bad situation here in Italy but since I follow American politics for a hobby I am really worried about the situation that may happen in America. Stay safe and keep your loved ones safe as well
You’re welcome. I really hope that the situations can get better for both of us. It’s so scary to see how fast those numbers are going up in Italy and the US.
18:59 "Excuse my little brace"
*draws absolutely perfect brace*
"It's really hard for me to do that"
🤣🤣🤣 19:55 " 'i' don't like to be on bottom. 'i' like to be on top"
I died momentarily when you said that.
This is brilliant! Well done! Thank you for all your hard work! I am busy with my 2nd year electrical engineering degree, and would not be passing the mathematics without your videos.
did you end up graduating with an engineering degree
Whoaaa omg this video will be the bible of Laplace transform!!! It just contains eveything! And your effort is really much appreciated in preparing these series of non-stop marathon! Thank you man!
You’re very welcome!!! Thank you for all your hardcore math problems on IG as well!
heyy!! I'm follow you on IG! really cool problems!
Through the link in the description, I've just learnt about a new way of solving differential equations, and now I can practice that method.
Just perfect! Thanks a lot!
You and your content are so cool!
Thanks
Please do a Marathon for Differential Equations 2nd Order. Your Videos about Integral and Dervivatives helped me soooo much. Thank you for the hard and impressiv work. Greetings from Switzerland :)
Since we're talking about diff eq. I'd like to request bessel function
47:45 When I took system theory course in university, my professor explained this property quite well. He described the dirac impulse as a rectangle with a width of 1/epsilon and a height of epsilon. For the limit of epsilon -> 0, this recantgle has a height of "infinity" and a width of zero, while the area (width * length) always remains 1.
Lies again? Lap Dance Transformers
*For the limit of epsilon -> inf
Is it weird to be a bit turned on by Laplace transforms?
yes
No
No its fine especially if you need to study this for exam
yes
I personally feel like a master of laplace transforms and I will check for mistakes!
I love your videos and i learn so much! Youre my favorite channel to watch math videos and tutorials! Keep up the good and fun work :D
Hi there, I wish you and your loved ones safe and healthy. Sincerely, 24/(1-x)
Dude! Let me finish the diff ep first???
The very same 2 u Steve...thanks a lot and for this great channel!
May I ask you if you can make physics video?
Are you a machine? God hell!
Kobe was your best friend?
Yes, everyone needs to watch Mu Prime Math's video on Laplace.
For your next marathon, I think you should do 100 different proofs of Quadratic Reciprocity.
Great job! I will watch it from the beginning to the end and do every exercise!
Wow, you used a clever and much much shorter way to find Laplace of sine and cosine than the conventional one I was tought! Thank you, greetings from Denmark :)
I remember bprp being one of my best resources for acing calculus 2 and a year later here we are with differential equations....Thank you for everything sir.
Happy to see you uploading a lot of new content. Nothing like some differential equations and laplace transform while im stuck at home due to covid-19.
Your energy is really amazing. The last time I got up and talked in front of a camera was many years ago, and that wasn't even for publication. Wonderful video.
@blackpenredpen thank you so much for this video! I am from the US and the university i attend got shutdown due to Covid-19 and classes are now done online. This is exactly what we are doing in Applied Engineering Analysis. You make learning from home so much easier! Thank you! 🇺🇸❤
Meticulous and excellent work. I have been watching your videos for a while now. your summary on Laplace transform is perfect. This is a condensed Bible and beneficial file, thank you
Excelente selección de ejercicios. El punto de inicio de todos ellos fue muy bien elegido para que fueran muy ágiles los cálculos.
Holy Moly, Your teaching style is totally different and everything is quite clear. Thanks a lot.
i woke up in the morning to this playing - thanks for blessing my dreams blackpenredpen
Infinite thanks you are a genius and I really appreciate your talent and dedication. This video is a jewel 💎
Just in time, this year I am going to have to learn this for signal and system analysis
You're a legend.
Keep up that amazing work.
Thank you so much bprp, my A-Levels have been cancelled and I don’t know if I am going to university this year. Your videos are kind of keeping me sane. Thank you :)
Great video. I've enjoyed it very much despite I've never done Laplace transforms :)
Answers:
1x1=1
1*1=t
L{(1-cos t)/t}=ln((s^2+1)^(1/2)/s)
integral from 0 to infinty of (1-cos t)/(te^t)=ln 2^(1/2)
really enjoy watching your tutorial man. Give me another hope not to give up on Differential Equations course.
I was in a Laplace Transform Marathon once. I finished in "la" place.
I just started to study laplace transforms yesterday. I think you are my prophet sir brbp.
Everything explained with details, the colored pens gives great sight of whats happening.
Great content 👍
1:43:43 There’s a mistake. It should be 6(s-2)^(-4)
[GD] 3xsiloN
Ahhhhh oh man >_<
However, I magically still got the right answer afterwards lol
I never thought you'd do it it's amazing thank u.
have a series and transforms exam in 2 days; this is exactly what i need
Perfect timing! xD
We're learning about these in class tomorrow for Differential Equations.
Loved the video! Could you evaluate the convergence of 24 different series?
It’s awesome to see how pure mathematics come to play in science fields like statistical mechanics where the Dirac delta function is represented by the normal distribution of a system as the number of microstates reaches Infinity so it makes sense that the integration over all states is equal to one in that context.
I have one day to study all of Laplace transforms before the exam!
Man!!! I needed this for my takehome assigments and quizzes due to lockdown. I can't thank you more than enough broooo
It's lawliet
This channel is my math teacher
Your voice is soothing, I am using this video as white noise while working on a flyer. I dont understand anything, but it lets me feel like I am doing something.
I remember I watched my first BPRP video two or three months ago and I literally fell in love with your dedication so that I watch your video everyday, even while I'm having lunch with my whole family. We all appreciate you and your sparkling joy! Greetings from Italy ❤️
I thought you'd start with "Yes, I'm serious. Today, we'll do 24 Laplace transforms and of course, we will do them in one take. I have the file here already."
Hello sir .. I'm happy to have been talk g much from your lectures. Long life to you
Having to stay home and learn DE , this video is going to push me through the finish line, thanks man going to buy some merch asap.!
Thank you! Hope all is well and best wishes to you and your loved ones
Thank you very much for your work!
Great one! Please consider a Fourier marathon too, thank you!
Wow. This is good. Finally finished the vid. Q17, so close to using Laplace to do fractional calculus.
Very helpful video! Thank you so much.
it's awesome when he does it laplace becomes fun
Thank you so much for a wonderful content!
I just love your passion! Thanks man! Emmanuel here, from Ghana
I'm teaching Laplace Transforms right now in my DiffEQ class. I'm going to post a link to your video.
Nice thanks!! I also have the pdfs on my site. Feel free to use them.
I actually love this video soo much
Wow i got everything in one shot for free love your session
It’s 12 pm on a Sunday and I just woke up to this playing on RUclips from auto play.
I get done taking my differential equations exam and this pops up, not today youtube
Wow laplace speed run, much wow
That was so much fun ! Isn't it?
if only this is available during my calculus days...so much helpful back in 2019 now....i just need light refresher
Just love your videos man!
this helped me so much omg. I understund now!!!!!!
im good thanks for asking, got exam in dynamical systems so, lot of laplace to do ay !
Hell yes another marathon! Lol sorry but these are best damn thing on youtube right now. Thanks brotha!
Exo you’re welcome! Glad you like it.
I love you bro honestly, stay safe
I shall be doing this for my math iii back paper. Thanks.
You done great deal for us @the brilliant man i have ever seen u and ur tag is so cool
Good video! Just a remark. The s variable is a complex number in the Laplace transform, therefore, the order relationship is not defined.
When you are expliciting the Region of Convergence (ROC) of the transforms, the conditions are over the real part of s: e.g. Re(s) > a
greetings from Chile, im taking Differencial Ecuations. I really enjoy your videos.Great JOB!!
I'm doing great, thank you for asking, made my day. Your videos explain everything so clearly and it's really helpful. Thank you for your hard work and I'm glad you are also doing well, even if this video is from a few years ago. You are amazing and a lifesaver!
ラプラス変換がよくわかりましたありがとうございます
I'm doing great! I'm studying at Panera with friends for our BIG midterm on monday.
WOW!!! Thank you so much for this upload
Thank you so much, it was an excellent lesson...
I loved this video, thank you :)
Good work, the Inverse Laplace would be very interesting indeed, while you are there it may also make sense to do Fourier Transforms as special case of Laplace mentioning the immense application of FT in our modern life and modern communication and imaging devices. Critical every day Technology that modern man cannot live without...
Again great job I enjoy your videos.
Cheers
But a>s almost never occur, because 0
Hey bprp, thank you once again for the amazing marathon, when everybody is really bound to stay home. I suggest that you do a video marathon on some other stuff like multivariable calculus or perhaps abstract algebra?
Thank you for your comment!
I think we need dr. P for that. I am very rusty in those topics.
@@blackpenredpen great way to become "unrusty"
We can also substitute gamma function in question 2, it makes it much easier.
That intro jump in was too lit 😎😁
Hey I really appreciate your hard work..thanks
Thanks! I enjoyed it
I have a test over this coming up! Thank you!
You’re welcome!!
omg me too, mine's tomorrow. good luck!
As someone who barely passed math, I have no idea how I ended up here.
cause when you pick a major, there's a low chance it doesn't include math as the background.
I was absolutely amazed with how you solved the problems. Thank you very much for this video.
Amazing focus you are a legend
Number 2 was a rather interesting approach to evaluate it for integer values of n. I never saw that one. Personally, I would have done a substitution to get the integral in the form of the gamma function for all real n ⩾ 0.
thank you so so much for this
Thank God you decided to do some Laplace Transforms when I’m taking Diff. Eq. 😭
Your hands are so strong and coordinated from holding that mic and switching markers for hours and hours.
I used to enjoy Laplace transforms and inverse Laplace transforms when doing this at uni.
I'm gonna do some kind of marathon while quarantined but it won't be record breaking lol
It's so nostalgic to look back at what I've studied in uni time...
I like all your videos. Thank you, learned a lot from you.
Fred Aelmans from the Netherlands
Thank you!!!
I love ypour content; you are the best youtuber!! thank you for you efforts for teaching and enthusiasm its very engaging!
Thank you!
50:00
No
For a>0 solution is e^-sa
For a=0 it is 1/2
For a