Laplace Transform: Second Shifting Theorem

[lovelplants]

love calculus.. so stressing.. hehe

[taeyeonitsumo91]

Thank you for posting up your videos (and your generosity for not making them private! :)), they are undoubtedly very helpful. How I wish some lecturers at universities could pick up a thing or two from you. God bless you and thank you once again. :)

[123modsam1]

very helpful video thanks alott

[xHollie92x]

I LOVE YOU!!! thanks for the help

[nemat90]

Brilliant!! Thank you sooo much!

[antonio12554]

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

[MrMymusicality]

I love it when at first you don't know something and something comes by like your video and all of a sudden the light turns on and every gear starts to grind right.... lol

[sanzo21]

YOU SIR, ARE A GOD.

[egymoha1]

thanks so much cris ! u really helped alot ! god bless u genuis

[judodude18]

Your videos are very helpful!

Do you have any videos of The Finite element method also? Those would help even more! Not only because your great at explaining, but it is also imposible to find anything of good substance about it online!

[prasanna046]

Dear Dr. Chris,

Very Helpful video.Your teaching style is very clear.Thanks for your time and effort.

This helps us a lot.

A student from RMIT Uni Melb:

[chalisblur]

Thank you for your very helpful videos Dr CrisTisdell ,

I really appreciate your time and effort into the video :)

[DoofersCreepers]

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

[thenickboy]

thanks for posting this - One question:

why do you convert f(t-1) => f(t)? this is what I keep getting lost on this shifting theorem. why are they equal to each other? thanks and keep up the good work!

[DrChrisTisdell]

@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, $f(t-1) \neq f(t)$ 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.

[FallofDarkness55]

Thank god, for people like you. I watch your videos, patrickjmt, and khanacademy videos. I love your teaching style. Keep up the good work.

[KO8789]

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

[DrChrisTisdell]

@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.

[eysteins]

Brilliant video.

many thanks from an engineering student in Norway.

[chiang0809466]

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

[tompatience]

@chiang0809466 +1; exactly the same situation until watching this - thanks! :)

[ssandar15]

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

[Sufman1]

thanks this was really helpful!

[graemepeo]

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

[livelife7890]

VERY helpful!

[Treshor]

You are amazing! Thanks so much for these videos. My circuits teacher really stinks at explaining things and I've never been exposed to laplace tranforms until his class.

[xXDrazicXx]

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

Thank you for this!

[HumanTargetAus]

UQ >> UNSW

[elsamr28]

Thank you so much, this was so helpful.

I would love to have you as my full time lecturer!

[themontybro]

brilliant work sir....!!!

ur videos r helping me a lot wid engineering mathematics...

thanks a lot...!!!

[alexmarrone8]

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

[macchesney]

Dr Tisdell,

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

[komy20790]

now I can go on with my assignment :)

[gematt7]

hah 30 mins before the exam.. GREAT HELP!

[MICHAELMEMISBACL]

If this vid makes me feel better about these problem, then that could = bravo, Chris!

[alina12100]

thanks dr it was great

alina from iraq  baghdad

[boscoboy2008]

Thanks for the vid, great help!

[pandalikesvin]

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

[stbaby57]

so do you always replace your function "stuff" with t?? so if i have the laplace trans of (t-1)u(t-1)....than the first t-1 will just be t?

[Shino2488]

what happens if ive got

[f(t-a) u(a)]

[SteveFlynn0]

yo chrizay to the tizday!

Nice work on the vid. A quick question, the table in the course pack has a few more transforms than the one that will come with the exam. Should we work on memorising those transofrms that won't be given? Or sleep easy at night knowing that we will be asked to derive or won't be asked at all for those xfroms NOT given.

Cheers

[DrChrisTisdell]

Hi Steve! Sleep easy - it's unlikely that we'll ask you to prove those kind of things.

[electriciansmate]

Hi chris, do you teach your students, the heaviside step function? Always amazes me about Mr Heaviside being an engineer and not a mathematician could come up the ideas. Brilliant!

[DrChrisTisdell]

Sure do Neil! In fact, I just spent a couple of minutes talking about Heaviside - the man. Not only was he a brilliant engineer, he also took "Maxwell's 20 equations on electricity and magnetism" and boiled them down to just 4 equations (which do not bear the name Heaviside). Good stuff!

[bluesrunthegame]

That's just ridiculous. No mathematician or engineer should rely that heavily on tables.

[DrChrisTisdell]

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.

[electriciansmate]

This brings back memories. To use the second theorem, is one thing. I proud to have known a fellow student who went out of his way to prove the second shift theorem. He is now working in Australia.

[DrChrisTisdell]

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.

[farahsho]

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 :)

[DrChrisTisdell]

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!

[kikk175]

Thanks for this chris, it really helped. Just in time for end of session exams too :)

[DrChrisTisdell]

Best of luck for your exam!