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.

Пікірлер: 154

  • @kaomachileshe4824
    @kaomachileshe48242 жыл бұрын

    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

  • @aaronbarragan8339
    @aaronbarragan83395 жыл бұрын

    Honestly out of 20 tutorials ive seen on this subject you were the only who explained understandable

  • @aaronbarragan8339

    @aaronbarragan8339

    3 жыл бұрын

    @Desmond Bronson you dumb dumb

  • @kadinmorse1
    @kadinmorse111 жыл бұрын

    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.

  • @litzymejia8817
    @litzymejia88172 жыл бұрын

    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!!!

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    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.

  • @electriciansmate1987
    @electriciansmate19876 жыл бұрын

    Great video, really got me going again while studying for the Fundamentals of Engineering exam. Thank you!

  • @xXDrazicXx
    @xXDrazicXx13 жыл бұрын

    Hey Dr Chris, I am a second year aerospace student in England and this has helped to clear things up! Thank you for this!

  • @Jenga368
    @Jenga36812 жыл бұрын

    Really well explained... Universities need more lecturers like you!

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    Many thanks and hope you also enjoy my new ebook. The free download link is in teh description.

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    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).

  • @ryanpurvis6617
    @ryanpurvis66172 жыл бұрын

    These 8 minutes cleared up 2 hours of trying to understand the textbook. Thank You!

  • @mono7891
    @mono789111 жыл бұрын

    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.

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    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).

  • @jferro96
    @jferro967 жыл бұрын

    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

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    Good luck with Laplace transforms. You can find more in my new ebook. The free download link is in the description.

  • @Prathap062

    @Prathap062

    5 жыл бұрын

    Sir can you send me the link please

  • @graemepeo
    @graemepeo13 жыл бұрын

    Thanks for putting this video up helped me understand the second shift theorem, just in time for my engineering math exam this tuesday!!

  • @DxROC
    @DxROC10 жыл бұрын

    Amazing video! Very clear and straight to the point! Thank you kind sir!

  • @macchesney
    @macchesney14 жыл бұрын

    Dr Tisdell, Thank you very much for this very clear and practical guide! your efforts are not in vein.

  • @sajidnajar3295
    @sajidnajar32955 жыл бұрын

    Thanks a lot you just really cleared my huge doubt about this second shifting theorem thanks a lot

  • @angkatanpw
    @angkatanpw12 жыл бұрын

    awesome lecture.. you sir are one the lecturer's i have seen who teaches with a smile...

  • @DrChrisTisdell
    @DrChrisTisdell11 жыл бұрын

    I am very glad to get your comment. Thanks!

  • @shehryarshabbir1352
    @shehryarshabbir13525 ай бұрын

    Great video just learned the second shift theorem.

  • @alexmarrone8
    @alexmarrone814 жыл бұрын

    Thanks for the videos. Just when you think you have finished all your mathematics in engineering it always works its way back in.

  • @DrChrisTisdell
    @DrChrisTisdell15 жыл бұрын

    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.

  • @sandar15
    @sandar1513 жыл бұрын

    Very nice teacher. I really love the way you show your knowledge. Keep on posting videos! Congratulations from Spain

  • @Wakeupfishy4
    @Wakeupfishy411 жыл бұрын

    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

    @negativexfinity6778

    2 ай бұрын

    Where you at now?

  • @Hamking1
    @Hamking112 жыл бұрын

    Haha, you sound so excited when you say "Laplace transforms" in the beginning :)

  • @aswinxi-b8756
    @aswinxi-b87565 ай бұрын

    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

  • @AJ-et3vf
    @AJ-et3vf2 жыл бұрын

    Awesome video sir! Thank you! Very understandable!

  • @098LMD
    @098LMD9 жыл бұрын

    You are brilliant!

  • @CharlesPieczonka
    @CharlesPieczonka7 жыл бұрын

    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)

  • @nurinsyuhada7768
    @nurinsyuhada7768 Жыл бұрын

    Thank You Dr Chris Tisdell! Have a good day ahead

  • @DrChrisTisdell
    @DrChrisTisdell11 жыл бұрын

    Excellent - such a good application. All the best with your studies.

  • @agyaanibong
    @agyaanibong13 жыл бұрын

    brilliant work sir....!!! ur videos r helping me a lot wid engineering mathematics... thanks a lot...!!!

  • @DrChrisTisdell
    @DrChrisTisdell13 жыл бұрын

    @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.

  • @vineethb88888
    @vineethb888888 жыл бұрын

    Sir, Thank you for very detailed classes... hope to have much more videos about fourier and z transforms.....

  • @chalisblur
    @chalisblur13 жыл бұрын

    Thank you for your very helpful videos Dr CrisTisdell , I really appreciate your time and effort into the video :)

  • @pradheepkrishna6964
    @pradheepkrishna696411 жыл бұрын

    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...!!!!

  • @dsppi4093
    @dsppi40933 жыл бұрын

    Nice Dr I love the explanation .

  • @kovalkeane6788
    @kovalkeane67883 жыл бұрын

    thank you for this. it has really cleared up my confusion regarding this type of problem

  • @jjtrick23
    @jjtrick236 жыл бұрын

    Awesome video. Subscribed. Thank you Dr. Chris Tisdell.

  • @DrChrisTisdell
    @DrChrisTisdell15 жыл бұрын

    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!

  • @meckskatehouse
    @meckskatehouse8 жыл бұрын

    This helped so much. Thank you.

  • @arvinbadillo5769
    @arvinbadillo57696 жыл бұрын

    thank you for the free ebook!

  • @elainaheraty2381
    @elainaheraty23816 жыл бұрын

    this was very clear, thank you!

  • @gloriathomas6499
    @gloriathomas64999 жыл бұрын

    thanks a lot for your perfect teaching

  • @DrChrisTisdell
    @DrChrisTisdell15 жыл бұрын

    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.

  • @augustin3400
    @augustin340011 жыл бұрын

    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

  • @kaizen1421
    @kaizen14219 ай бұрын

    Thank You Sir , You Nailed It.

  • @ericshun3011
    @ericshun30113 жыл бұрын

    Good on you for making this, love having an Aussie for once!! Cheers , 21yr old ENGG student

  • @cruxifier1
    @cruxifier13 жыл бұрын

    Very clear well done sir 👍

  • @dylansheridan2892
    @dylansheridan2892 Жыл бұрын

    Thank you for your videos. God bless.

  • @MrPalmmmmy
    @MrPalmmmmy9 жыл бұрын

    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

  • @Hamking1
    @Hamking112 жыл бұрын

    Btw, I just got my grade back on my final in diff.eq&lin.alg ... 91.33%! Understanding the step function really helped! Thanks :-)

  • @chiang0809466
    @chiang080946613 жыл бұрын

    thanks a lot !! it's burning my brain until i see this vid~thanks again!!

  • @zuhairalsaffar7001
    @zuhairalsaffar70012 жыл бұрын

    How could I thank you you did your best to make it easy

  • @KO8789
    @KO878913 жыл бұрын

    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

  • @BlueCasts
    @BlueCasts11 жыл бұрын

    Thanks, Fantastic Explanation

  • @Abukhadir1
    @Abukhadir111 жыл бұрын

    thank you so much prof. you are a really great....i'm fully understand of what the laplace transform SST is

  • @PWDr93
    @PWDr9312 жыл бұрын

    tomorrow actually! I'm well set so expecting good results! :) Thanks a lot!

  • @jeffstrueby9369
    @jeffstrueby93696 жыл бұрын

    Well explained. Thanks!

  • @angkatanpw
    @angkatanpw12 жыл бұрын

    thanx for the link sir.. this website will help me in my mechanical engineering career..:D

  • @mcnojoke127
    @mcnojoke1277 жыл бұрын

    Thanks. Im starting to understand it now.

  • @farahsho
    @farahsho15 жыл бұрын

    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 :)

  • @kingdc7017
    @kingdc7017 Жыл бұрын

    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.

  • @antonio12554
    @antonio1255412 жыл бұрын

    i love the way your explain i wish my tutor could do that. is help me a lot

  • @noelcruz2932
    @noelcruz293210 жыл бұрын

    Thanks. :D I appreciate the free lesson.

  • @DrChrisTisdell

    @DrChrisTisdell

    10 жыл бұрын

    My pleasure.

  • @DrChrisTisdell
    @DrChrisTisdell11 жыл бұрын

    You are very welcome.

  • @isurudilshan7172
    @isurudilshan71722 жыл бұрын

    Thank you very much sir..

  • @SM2904R
    @SM2904R4 жыл бұрын

    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)?

  • @webster951
    @webster9518 жыл бұрын

    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?

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    My pleasure!

  • @inthebackwiththerabbish
    @inthebackwiththerabbish Жыл бұрын

    you sir are a genius

  • @Mihokawano
    @Mihokawano9 жыл бұрын

    great explaining..you should be my math teacher :p

  • @aly271092
    @aly27109211 жыл бұрын

    this video was awesome :) I learned much more I did in class! I may not fail my exam now XD

  • @DrChrisTisdell
    @DrChrisTisdell13 жыл бұрын

    @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.

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    Best wishes to all in Germany and thanks for your comment!

  • @HYITHO
    @HYITHO12 жыл бұрын

    thanks heaps Dr.Tisdell!!!!!

  • @aliyeganeh5871
    @aliyeganeh58714 жыл бұрын

    thanks a lot it was very helpful

  • @HarshitNiel
    @HarshitNiel10 жыл бұрын

    that was really helpful, thanx a lot!! :D

  • @ngkean9743
    @ngkean97433 жыл бұрын

    how to do if the (t-1) is different or in other word, not using second shifting theorem. Please reply me back

  • @livelife7890
    @livelife789013 жыл бұрын

    VERY helpful!

  • @nemat90
    @nemat9012 жыл бұрын

    Brilliant!! Thank you sooo much!

  • @jasema5978
    @jasema59787 жыл бұрын

    thanks a lot

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    My pleasure - good luck with Laplace transforms.

  • @DrChrisTisdell
    @DrChrisTisdell11 жыл бұрын

    Well done!!!

  • @angkatanpw
    @angkatanpw12 жыл бұрын

    ok thanx sir.. i'll download it..

  • @TheTalmon18
    @TheTalmon188 жыл бұрын

    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 :[

  • @pandalikesvin
    @pandalikesvin14 жыл бұрын

    Thanks, this helps me a lot. Great video, keep it up. peace out.

  • @mohamedalimarmouri7771
    @mohamedalimarmouri77719 жыл бұрын

    You are my hero god bless you

  • @basilagula9977
    @basilagula99779 жыл бұрын

    Right on but then cos[3(t-1)] to cos3t. how did that happen.

  • @lamrex18

    @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))

  • @TheProfessorDen
    @TheProfessorDen12 жыл бұрын

    Wow, thank you so much! My text book was not explaining this well at all and my prof did a poor job with it.

  • @DrChrisTisdell
    @DrChrisTisdell12 жыл бұрын

    Thanks again!

  • @bonita799063
    @bonita79906311 жыл бұрын

    any chance of moving to Melbourne ( RMIT UNIVERSITY) may be?????? , thanks a lot sir

  • @TheTalmon18
    @TheTalmon188 жыл бұрын

    What happens if the shifting doesnt match? For example, I had to convert a piecewise t/2 0

  • @huihui666

    @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)

  • @DoofersCreepers
    @DoofersCreepers13 жыл бұрын

    very very helpful, thank you. Vic student Wgtn NZ.

  • @nathangething6418
    @nathangething64182 жыл бұрын

    This is so helpfull thanks

  • @hams7716
    @hams771610 жыл бұрын

    Why replace the (t-1) and come only t?

  • @Raz0880

    @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?

  • @browniebro6183
    @browniebro61835 ай бұрын

    Thank you so much ❤️🙂

  • @silvernitrate5608
    @silvernitrate56084 жыл бұрын

    Thank you👍🏻