Laplace Transform: Second Shifting Theorem
Free ebook tinyurl.com/EngMathYT
I calculate the Laplace transform of a particular function via the "second shifting theorem". This video may be thought of as a basic example. The second shifting theorem is a useful tool when faced with the challenge of taking the Laplace transform of the product of a shifted unit step function (Heaviside function) with another shifted function. The Laplace transform is very useful in solving ordinary differential equations. Such an example is seen in 2nd year mathematics courses at university.
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honestly words may fail to express how thankful i am for this kid of explanation, you're simply the of all lectures have seen on this topic
Honestly out of 20 tutorials ive seen on this subject you were the only who explained understandable
@aaronbarragan8339
3 жыл бұрын
@Desmond Bronson you dumb dumb
Thank you so much. It's people such as yourself who give their time to make tutorial videos that are helping me get through my degree.
I never usually comment under a KZread vid for math but omg after so many countless videos, this is literally the only video that breaks down on how to use the second shifting thm. THANK YOU SO MUCH!!!
Glad you found this useful. You might also like to check out my new ebook, which is something I am experimenting with. The free download link is in the description.
Great video, really got me going again while studying for the Fundamentals of Engineering exam. Thank you!
Hey Dr Chris, I am a second year aerospace student in England and this has helped to clear things up! Thank you for this!
Really well explained... Universities need more lecturers like you!
Many thanks and hope you also enjoy my new ebook. The free download link is in teh description.
Thank you! You might also like my new and free ebook, which has many more examples. It is freely available from bookboon.com (the link is on my YT channel).
These 8 minutes cleared up 2 hours of trying to understand the textbook. Thank You!
Dr. Tisdell, your explanation is really great. My professor is also good but your method is crystal clear. Thank you for helping so many like me.
Thanks. If you enjoyed this video the you might also like my new and free ebook, which has many more examples. It is freely available from bookboon.com (the link is on my YT channel).
I love you man, i had zero idea how to do this and now i feel really good about it. youre website and videos helped me out a lot. i appreciate it
Good luck with Laplace transforms. You can find more in my new ebook. The free download link is in the description.
@Prathap062
5 жыл бұрын
Sir can you send me the link please
Thanks for putting this video up helped me understand the second shift theorem, just in time for my engineering math exam this tuesday!!
Amazing video! Very clear and straight to the point! Thank you kind sir!
Dr Tisdell, Thank you very much for this very clear and practical guide! your efforts are not in vein.
Thanks a lot you just really cleared my huge doubt about this second shifting theorem thanks a lot
awesome lecture.. you sir are one the lecturer's i have seen who teaches with a smile...
I am very glad to get your comment. Thanks!
Great video just learned the second shift theorem.
Thanks for the videos. Just when you think you have finished all your mathematics in engineering it always works its way back in.
H Neil - great to hear from you again! I'm sure that you could prove the SST if you wanted to. The proof just relies on a simple substitution for $(t-a)$ in the integrand.
Very nice teacher. I really love the way you show your knowledge. Keep on posting videos! Congratulations from Spain
You are brilliant! I had been sitting here clueless, staring at my homework trying to make sense of all this and NOW I get it! Thank you, thank you, thank you!
@negativexfinity6778
2 ай бұрын
Where you at now?
Haha, you sound so excited when you say "Laplace transforms" in the beginning :)
It's been 14 years of this video I'm been helped by this today I'm passed today because of this , thanks brother ❤️ keep going
Awesome video sir! Thank you! Very understandable!
You are brilliant!
What do you do when the values in the brackets aren't the same? for example one is just t, and one is (t-1)
Thank You Dr Chris Tisdell! Have a good day ahead
Excellent - such a good application. All the best with your studies.
brilliant work sir....!!! ur videos r helping me a lot wid engineering mathematics... thanks a lot...!!!
@KO8789 Yes. Usually (at least at UNSW) the 2nd shifting theorem is part of a Laplace transform table that students will have with them during exams. Hope this helps.
Sir, Thank you for very detailed classes... hope to have much more videos about fourier and z transforms.....
Thank you for your very helpful videos Dr CrisTisdell , I really appreciate your time and effort into the video :)
Sir thank You soo much.!!!!! Am scoring good in my Maths test because of you Moreover gained lots of knowledge....Thanks alot...Hope I get a chance to meet you!!!!Am from India,Hope you vist India for this kind of lecture classes and rock us...!!!May god bless You...!!!!
Nice Dr I love the explanation .
thank you for this. it has really cleared up my confusion regarding this type of problem
Awesome video. Subscribed. Thank you Dr. Chris Tisdell.
Hi Farahsho: This video is a really simple example. The more invovled transfrom problems are (a) more time consuming; and (b) take up more board space. Thus, it is not always possible to "fit" a detailed solution and explanation into a short video (espcially with Fourier series) - but I'll try!
This helped so much. Thank you.
thank you for the free ebook!
this was very clear, thank you!
thanks a lot for your perfect teaching
Blues: I'm not sure what you mean when you say "rely that heavily on tables". Can you please explain a bit more? I've been a professional mathematician for almost a decade and the use Laplace transform tables in day to day calculations of more significant problems is the standard. They are handy. I think it would be very time consuming to derive transforms from first principles again and again in daily use. Of course, it does not hurt to be aware of the derivations of such transforms.
i was getting scared on hearing the name "LAPLACE TRANSFORM" ... wow... but now.. i am loving it ... all because of you sir .. thanks a lot
Thank You Sir , You Nailed It.
Good on you for making this, love having an Aussie for once!! Cheers , 21yr old ENGG student
Very clear well done sir 👍
Thank you for your videos. God bless.
thanks alot teacher.By the way im Thai student. Thanks for uploading this video because this video fix my mathematics problem that my teacher cannot teach me to understand it. Thk alot
Btw, I just got my grade back on my final in diff.eq&lin.alg ... 91.33%! Understanding the step function really helped! Thanks :-)
thanks a lot !! it's burning my brain until i see this vid~thanks again!!
How could I thank you you did your best to make it easy
Dear Dr Chris, when you say/write ''We apply the second shifting theorem'' on the board mean that formula is from data book as wells? Cause I was trying hard to understand how to get expt^-a*s by looking at the equation (LHS) without refer to data book. Cheers
Thanks, Fantastic Explanation
thank you so much prof. you are a really great....i'm fully understand of what the laplace transform SST is
tomorrow actually! I'm well set so expecting good results! :) Thanks a lot!
Well explained. Thanks!
thanx for the link sir.. this website will help me in my mechanical engineering career..:D
Thanks. Im starting to understand it now.
Thanks chris for the video,it really helped me a lot.I would be more happy if you would upload some difficult problems from laplace and fourier series :)
What a Lord! this was so simple after seeing his explanation. How my uni professor explained it was so hastily and vaguely put that It was incredibly hard to actually understand what was happening.
i love the way your explain i wish my tutor could do that. is help me a lot
Thanks. :D I appreciate the free lesson.
@DrChrisTisdell
10 жыл бұрын
My pleasure.
You are very welcome.
Thank you very much sir..
How should one go about when we have the product of a function g(t) and the unit step function U(t-a) when g is not in the form g(t-a)?
I am doing tu(t-4), I used your method and I got e^-4s x 1/s^2. But the answer also has a 4/s, could you explain why?
My pleasure!
you sir are a genius
great explaining..you should be my math teacher :p
this video was awesome :) I learned much more I did in class! I may not fail my exam now XD
@thenickboy I think you are getting a little mixed up with the algebra. In this problem we want to identify the function $f$ so that we can find its transform $F$ (and then multiply $F$ it by $e^{-as}$ to get the final result). The $f(*)$ here is $cos 3*$ where the $*$ is any independent variable. Now, $f(t-1) eq f(t)$ however, the function $f$ doesn't change - it's still $f(*)= cos 3*$ . That's the important thing - you're trying to find $f$ and then transform it.
Best wishes to all in Germany and thanks for your comment!
thanks heaps Dr.Tisdell!!!!!
thanks a lot it was very helpful
that was really helpful, thanx a lot!! :D
how to do if the (t-1) is different or in other word, not using second shifting theorem. Please reply me back
VERY helpful!
Brilliant!! Thank you sooo much!
thanks a lot
My pleasure - good luck with Laplace transforms.
Well done!!!
ok thanx sir.. i'll download it..
What would L{t*u(t)} be? Would a = 0, so it'd be e^0 * L{t} which is just 1/s²? Doesn't seem right to me :[
Thanks, this helps me a lot. Great video, keep it up. peace out.
You are my hero god bless you
Right on but then cos[3(t-1)] to cos3t. how did that happen.
@lamrex18
9 жыл бұрын
Probably too late but you get that from the definition of the second shifting theorem - L(u(t-c)g(t-c)) = e^(-cs).L(g(t))
Wow, thank you so much! My text book was not explaining this well at all and my prof did a poor job with it.
Thanks again!
any chance of moving to Melbourne ( RMIT UNIVERSITY) may be?????? , thanks a lot sir
What happens if the shifting doesnt match? For example, I had to convert a piecewise t/2 0
@huihui666
8 жыл бұрын
+TheTalmon18 theres a modified shifting for the cases you mentioned. For the special case where you dont have a function f but just u(t-6) like you mentioned above, just think of f(t-a) = 1, and we all know the laplace of f(t)=1 is 1/s. Therefore, for the last term it should be (3*e^-6s)/s. As for the case where the function f has a different shift compared to u(t-a); you use the exact same theorem;except the laplace of f(t) becomes the laplace of f(t+a), where a is the shift from the unit step function. so for example L{tu(t-2)} = e^(-2s)L{(t+2)} = e^(-2s)(1/s^2 + 2/s)
very very helpful, thank you. Vic student Wgtn NZ.
This is so helpfull thanks
Why replace the (t-1) and come only t?
@Raz0880
9 жыл бұрын
***** hmm.. Still, didn't understand why? Do you have a link or a video to explain this? I thinking if you get (t-2) = 2t?
Thank you so much ❤️🙂
Thank you👍🏻