Initial Value Problems with Laplace Transforms (KristaKingMath)

► My Differential Equations course: www.kristaking...
Initial Value Problems with Laplace Transforms calculus problem example.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@celestereyes4834]

You have literally singlehandedly helped me get through a semester of both Calc III & DE. Your way of teaching is such a perfect match for my way of learning & I appreciate these videos so much!

[@redeagle8864]

Again, thank you so much. I feel like I keep winning the lottery every time I click on one of your videos.

[@kristakingmath]

+Fred Okafor lol, love that! I'm glad you're finding them helpful.

[@yibrahgebru]

flawless step by step. This is the best videos I have ever watched in the Laplace Transform topics.

[@kristakingmath]

Thanks for the comment! I'm so glad I can help. :)

[@ProMichael247]

Super helpful! My teacher is very hard to understand and has horrible hand writing! These videos have helped a bunch. Thanks

[@kristakingmath]

I'm so glad they're helping! Thanks for letting me know. :)

[@mohan153doshi]

Fantastic explanation - never had seen Laplace transform explained so neatly and succinctly. Your videos are just awesome. Thanks a lot.

[@kristakingmath]

Thank you so much, I'm glad you liked it! :D

[@kristakingmath]

I will definitely continue! Thanks for the kind words. :)

[@mindshare-revisitingmyappr6533]

You have so much patience..Kudos to your teaching style..the way you explain each and every small thing is really helpful..

[@kristakingmath]

Thank you, Tushar!

[@ZAKPARKOUR]

I have an engineering exam tomorrow morning, Thank you for making this content! It's helped me an amazing amount :)

[@kristakingmath]

Good luck on the exam!

[@ZAKPARKOUR]

This topic featured in the exam and i nailed it thanks to you! thanks so much.

[@kristakingmath]

Awesome! So glad to hear it! :D

[@amthi]

Thanks so much. I have an exam tomorrow and seeing everything worked out from start to finish really helps. I followed along step by step and I feel a lot better now.

[@kristakingmath]

You're welcome! So glad you liked it! :)

[@sreeharimadhu6885]

Thank you Krista. I was not confident about solving these type of questions, but after watching your video I feel much better. Cleared my doubts well.😊

[@kristakingmath]

You're welcome, I'm so glad it helped! :D

[@slimthephoenix]

Thanks! These types of problems can get confusing very quickly.

[@baburo101]

I love the classical blackboard and chalk software. Cool. Thanks for the help.

[@caribbeankpoplover]

Wow, I probably would have never viewed LaPlace as "not so hard" if I didn't get help from your videos! Thank you~^-^

[@kristakingmath]

I'm so glad the videos are helping!

[@FRIENDSForever-hh7dh]

i really understood the whole concept . you are really good teacher. Thanks a lot

[@RandyLott]

@TheIntegralCALC Somewhat. I graduated from my previous college and this was my first semester at this university, which is why it's difficult. I've used youtube and online books for help, but it's still a little confusing. I do understand why I would want to find the frequencies and magnitudes/phase of the components of a composite waveform, though. This is definitely used in digital signal processing.

[@kristakingmath]

Oh good, I'm so glad! Good luck on your exam!! :D

[@kristakingmath]

Glad I could help!

[@dorianclare4681]

Jan 2021 and this video is still super helpful. Thank you.

[@kristakingmath]

They definitely can! Glad this helped! :)

[@kristakingmath]

Hooray! Congratulations! :) Good luck with whatever you have planned next. :)

[@kristakingmath]

@fingerboy18 Have you been able to make some good progress though?

[@MG-hi9sh]

I’m very happy I got the right answer for this. It took a lot of working out.

[@Pac2Man]

You're a genius. Extremely well explained.

[@kristakingmath]

I'm glad you like my style! :)

[@matheusmacedo5265]

wish I found your channel ealier :p real clear explanation, thanks a lot!

[@FahimMotoGP]

You're the best. This was my last class before graduation. Now I'm done :P

[@RandyLott]

Still working on my linear time-invariant systems. It's really hard to relate it to what I know already. We use Laplace and Fourier Transforms often :(

[@connorminx8830]

This is awesome. Had I known about this earlier on I would have strongly considered buying the 27$ sub to your website for difeq, if this is any proof of quality therein I have no doubt it would be worth the price

[@chrisriker4969]

Are the values of f'' and f' always going to be the same for every Laplace transform problem, or does it differ depending on the original differential equation?

[@kristakingmath]

@mercy777ish Daniel, YOU are so sweet! :) I hope 2012 is the best year ever for you! :D

[@kristakingmath]

@baburo101 Hey thanks! And you're welcome! :D

[@a7kc]

I'm confused at 17:56 when you say you have to do 2!/2! in the numerator. Im confused why it isn't just 2! in the numerator because n=2 in that case

[@kristakingmath]

a7kc Because that would change the value of the numerator. Multiplying by 2!/2! is like multiplying by 1, which doesn't change the value.

[@MrPetisebok]

if I need to find for example y^n(y+3), How do I do that? according to the formula it is s^n F(s)-s^n-1 f(0)-s^(n-2) f'(0)...-sf^(n-2) (0) -f(n-1) (0). what do I do with ....?

[@tayloreckert3257]

You are such a great teacher

[@kristakingmath]

Thanks!

[@terrencemadanhi8833]

Thank you Krista you are good keep it up

[@kristakingmath]

Haha thanks! And I'm glad the video was helpful! :D

[@GarNBer]

Thank you so much, it was much easier to understand. Thanks.

[@kristakingmath]

thank you so much! :)

[@enderslayer2111]

thank you so much if i had money i would have pay you for the help tbh keep it up

[@Arglflargl]

Hello, pleeeease make me a video!! i have an initial value problem here that i'm so stuck on, i can do it down to the part where i have to bring fractions over & combine them, i just get stuck from there on! the question is: d^2y/dx + y = 1. Thanks :) argl

[@ifoxrider]

what's happen if you run into the case where your denominator is s^2+s+1. Do you use quadratic equation? It will be ugly as hell to spoil it out

[@carultch]

If you get a denominator that is an irreducible quadratic, this means you complete the square to make sense of it. The inverse Laplace transform will be a linear combination of sine and cosine, both multiplied by an exponential decay term. As an example, consider (s + 7)/(s^2 + 2*s + 5) I picked this one so it would simplify without fractions or square roots. Complete the square: (s + 7)/((s+1)^2 + 4) Regroup the numerator, so that the denominator's squared function of s (prior to squaring) appears as a term in the numerator. ((s+1) + 6)/((s+1)^2 + 4) Also rework it, so that the square root of 4, appears as a factor of the remaining constant in the numerator: ((s + 1) + 3*2)/((s+1)^2 + 4) In general, the first shift theorem tells us the following: L{e^(a*t)*f(t)} = F(s - a) Where F(s) is the Laplace transform of f(t), and a is the exponential growth constant This means: L{e^(a*t)*cos(b*t)} = (s - a)/((s - a)^2 + b^2) L{e^(a*t)*sin(b*t)} = b^2/((s - a)^2 + b^2) For us, we can recognize that a = -1 and b = 2. Thus: ((s + 1) + 3*2)/((s+1)^2 + 4) = L{e^(-t) * cos(2*t)} + 3*L{e^(-t) * sin(2*t)} Thus the solution for the inverse Laplace is: e^(-t) * [cos(2*t) + 3*sin(2*t)]

[@danielnatale6130]

You are the biggest help!

[@kristakingmath]

+Daniel Natale Thanks!

[@fazlinabasri3152]

tq krista!u have been of great help! :)

[@kristakingmath]

Thanks! I'm glad I could help!

[@belalibrahim7501]

Thanks alot , u made our live easy

[@kristakingmath]

+Belal Ibrahim You're welcome, I'm glad it helped!

[@Ishaqsaqi007]

Thanks alot! Although it helps me but I wants bit more like inverse of laplace and inverse of laplace in product under different condition. It will be your affection if you help me out through your helpful tuotorials to sought out that problem. I will send u the exact topics which is creating problems for me to understand them so that you may help in the better way! Thanks again for paying attention to my request!

[@pauloesperon7697]

you are great... thank you again.

[@kristakingmath]

+Paulo Esperon You're welcome!

[@MrRaohm]

Hello, I'm a mechanical engineering student and I find your videos very useful! I started to see them since high school when I was teaching myself Calculus 1. I wonder what programs and tools you use to do those videos (that chalkboard with the precise handwriting), I've been wanting to do that as well (I live far from home and my sister who is in high school needs me to help her with math and physics). Thanks!!!

[@kristakingmath]

I explain here :) www.kristakingmath.com/my-videos

[@password6975]

extremely helpful indeed

[@beneya]

thank you for your explanation. Maths

[@aizazullah952]

great job ...............thank u soo much

[@shreyanjitgupta7159]

Great video... Hope you don't mind but you and patrickJMT, you two sound alike a lot.

[@michaelcastro9977]

Thank you very much! U ROCK!

[@kristakingmath]

Thanks!!

[@alexclark5325]

Hi Krista, what software and hardware do you use for the screen recording?

[@jessenunez1718]

thank you so much!!!

[@kristakingmath]

You're welcome, Jesse! :D

[@hmmusic6417]

THANKS !!!

[@kristakingmath]

You're welcome, HM!! :D

[@HassanHijazi1995]

Thxxx a lot, rlly appreciated :)

[@kristakingmath]

Glad you liked it! :)

[@phinpheen7541]

Thanks

[@kristakingmath]

You're welcome, Phin!

[@lillyel2824]

arigatooo sensei 🧡

[@kristakingmath]

You're welcome, Lilly! :)

[@abhaykumar-dt5yl]

can ny1 tell me...how c calculated the value of A,B,C,D

[@melih96melih]

look up Partial Fraction Decomposition

[@dpmike32819]

That was beautiful

[@mmusa6486]

This video isa awesome

[@blackoperations9895]

wow

[@Mrbaliya.]

My problem is this partial fraction

[@arsevela33]

People just dont get it!! Beggars arn't choosers... its amazing to me how they still wine about needing a specific problem just for them... and saying "I want more of these..." rather than suggesting.. these tutors are doing us a favor. so get off their backs!

[@maniys]

thank yoooo :D

[@kristakingmath]

You're welcome, Ruchira! :D

[@hamdikoraim8188]

god work

[@aLQuarter]

+Ibrahim Karim good*

[@jgreen9381]

The presentation is great. I just feel it's a little over explained. If someone doesn't know how to isolate a variable by dividing, and they are in a differential equations class solving Laplace transforms they are in for a world of hurt. That really is my only criticism

[@fatinamirah4426]

subtitle line is disturbing my sight

[@bhag446]

U looking beautiful

[@Bitapigeon]

You smart beautiful girl! I love you! :)

[@kristakingmath]

I love you too! :D

[@jiberuba8856]

Krista King hi need your help about this problem

[@musaabdulhamid5037]

please can you be my girlfriend ... with you by my side i will never fail again