Laplace Transforms and Integration by Parts with Three Functions (KristaKingMath)

[@blackpenredpen]

A viewer of mine (Jem) sent me here and I watched this video! I can only say "WOW"! Very well-made and well-explained! Keep up the great work Krista!

[@kristakingmath]

Thank you so much! Right back at ya, you're doing great work! :D

[@kristakingmath]

the hyperbolic sinh and cosh functions don't behave the same way as sin and cos. with the hyperbolic functions, the derivative of sinh is cosh and the derivative of cosh is sinh. if you continue taking derivatives they just alternate back and forth between these functions. there are no negative signs involved. hope that helps clarify! :)

[@bdelahunty]

Euler's formula, cosh(x) = (e^x + e^-x)/2, simplifies the integral so you only need to integrate by parts once

[@ahmedalqutaini8553]

My college degree should be stamped and certified by Krista !! she gave me so many ahaaaaa moments !!! since percalc and now I am taking diffeQs !!! good job girl !!

[@kristakingmath]

I'm so glad I've been able to help along the way! :D

[@tambuwalmathsclass]

This is beautiful. I love platform (app) use in making this tutorial.

[@kristakingmath]

Glad you like it!

[@azmath2059]

really good work Krista!! I watched the whole 25 minutes. There's only one thing........ You need to prove the limits to infinity more rigorously using L'hopitals Rule. Lim t->inf te^-t = Lim t->inf e^-t = 0

[@mashfique1]

thankx .....there are alot of calc vids....most does the easy ones.....very few explains such complex ones like you

[@kristakingmath]

+mashfique1 I'm glad you like them!

[@tonpituwai963]

awsome presentation..i just love every bit of it...dosnt matter how tedious is it, as long as i learnt someting that could never forget..thanks alot Krista

[@sachitkatri6019]

thanks you helped me 6hrs before my exam gbu !

[@kristakingmath]

Happy holidays to you as well!

[@alexv2053]

thanks i really needed help doing integrals that are a product of three functions

[@FILIPEB777]

Thanks made my life easier!!

[@kristakingmath]

Glad I could help! :)

[@sakuragrl08]

What a beastly problem! Thank you for this great video.

[@zeek1116]

finished watching all the videos, practiced all your problems on top of the ones in the book, thank you sooooo much! i feel much better about today's final than i did 2 days ago :)! If only I found you earlier in the qtr ahahahah! Thanks again :)!

[@mahmoudwaheed1879]

nice work ! but i have a little objection ... when we substitute with the limit ( infiinity ) we find that it will give 0*inf due to the t*e^-st term and therefore it cant be equal to 0 and it must be solved by " l'hopitals rule " .. check it and respond .. and im really happy that there are still people who waste their time just to help other people .. thank you !

[@Dtinsider]

This video was exactly what i was looking for. Thanks!!

[@kristakingmath]

I'm so glad it helped! :D

[@albertbii6514]

You can differentiate the laplace transform of -(tcosh(3t))

[@nicogehren6566]

very well explained. thanks

[@carloss3534]

Great video. I now get the fact that LT is only about integrating skills.

[@lhaellor]

Please one thing, in 11: 20 -- 11:50 ( How did you do the inverse? , can you show full explaining? please! I could not understand )

[@kristakingmath]

Oh no!! I'm sorry the test didn't go how you hoped, sometimes that happens. :( Hopefully it was hard for everyone else and the curve is really good!! :D

[@terrawulf]

Thanks a lot!! Worked out this problem n on the 4th trial I got the right answer, did a very silly mistake. Anyways 'twas worth the mistake. Thanks once again. Keep up the good work.

[@kristakingmath]

:D

[@terrawulf]

Krista King Hi! Do u have any videos related to Series and basic geometry like parabola, hyper bola etc?

[@Luffy-hh4tj]

thank you for this video 😊

[@jackbungart6666]

if i had an instructor as cute as you i would probably try a little harder ;) your videos are amazing too. thanks for all the help :D

[@RabeeQiblawi]

Thank you >> I have a final exam in differential equations tomorrow ... for the third time

[@zeek1116]

your way of teaching helped alot....the test however was horrible! lol lets hope he curves very generously :)

[@robertherbert8419]

...impressive...maybe using the DI method might be less tedious selecting e^-st(t) in the D column and cosh 3t in the other.column.

[@bernardpaulo3814]

Hi , your video is amazing

[@kristakingmath]

Hope it went well! :)

[@jemcel0397]

Hey Krista. I was just wonderinng, can you do a version of this using Euler's Formula? I'd would be nice if you can.

[@thies2us]

You must really love to help otherwise, you would not have gone through this tedious integration. Professors do not even do this in class.thanks

[@bonkuschan]

Thanks ...been trying to look for a solution for something like this, but at around 3.50 differentiate cos 3t becomes 3sin 3t dt...should it be -3sin 3t dt??

[@talalelmasri6343]

Thank You

[@kristakingmath]

You're welcome! :)

[@shubhammishra8090]

Can't it be done by writing cosh3t as (e^3t +e^-3t)/2 ?

[@AhsanAli-jw3nd]

is du =-3 sinht3t .dt instead of du =3 sinht3t .dt at 4:15

[@AhsanAli-jw3nd]

@krista king

[@AhsanAli-jw3nd]

krista king

[@kristakingmath]

No, the hyperbolic functions are different than regular trig functions. You're right that with regular trig functions the derivative of sine is cosine, and the derivative of cosine is -sine. But with hyperbolic functions, the derivative of sinh is cosh, and the derivative of cosh is sinh. There's never a negative sign introduced. You would think they would be the same as regular trig functions, but they aren't. I hope that helps! :)

[@AhsanAli-jw3nd]

Thanks krista King

[@AliHaider-jx7nx]

Very Nice

[@StuartBarter]

I just watched the whole thing.... horri shiiiiiii- that's long...... Very thorough thanks

[@LDixon007]

Or, you could write cosh 3t in terms of the exponential function, etc....

[@ibenagumuchennacallistus8233]

please, can u help me with the integral of tsin2tcos(tsint) w.r.t t

[@kristakingmath]

sketchbook combined with a wacom pen tablet. :)

[@kristakingmath]

Not sure to be honest.

[@mireyarochavejar1812]

But the derivative of cos isn't it -sin, instead of +sin?

[@Charlietheleet]

suprised myself by actually understanding whats going on here o.O but what do engineers do with functions like this?

[@carultch]

Control systems is one such application You are trying to control a system that has its own dynamics, and you'd like it to settle on a setpoint as quickly as possible. Suppose it were a motor, that were trying to move a machine part to a specific position. But that machine part has its own inertia and its own friction, so the motor voltage you apply doesn't directly control its position. Instead, depending on the details of how the motor controller interacts with the dynamics of the machine, the machine part could follow an exponential decay, or could oscillate back and fourth, or a combination of both. Or if it is unstable, it could overshoot its target and continue to get worse. These functions like sine, cosine, exponentials, cosh, and sinh, are typical behaviors of how such a machine part would respond to a sudden step input to the motor. The goal is to determine the details of the controller, that get it to respond as fast as possible, while minimizing properties like overshoot, oscillations, and instability.

[@Charlietheleet]

11 years ago was just starting my journey. Thanks for your reply though !

[@eduardopaz1866]

i love ur voice :D

[@zepedacanojessicadelcarmen4514]

love u

[@johnjones6964]

you left out v from your first integration by parts, cosh*-1/s*e^(-st)+(s/t) integral............

[@kristakingmath]

wouldn't that be nice? unfortunately, it won't work! :(

[@kristakingmath]

:D

[@vincejiang2065]

SAVED MY BUTT!!!!!

[@zeek1116]

final in t-minus 4 hours! ahahha

[@vivaishah]

omfg, why cant we just use product rule to integrate that thing?

[@carultch]

There is no such thing as the product rule for integration. The closest we have, is integration by parts, which is derived from the product rule, but isn't a perfect product rule that allows us to integrate any product of two elementary functions.

[@VPG2901]

Such kind of math problems are to test your skill or patience ? XD

[@turtle1361]

What is this useful for? building airplanes? Sorry to ask I am in high school.

[@carultch]

Yes. Building airplanes is one such example. The autopilot controller is designed with the theory of differential equations. The vibration characteristics of the wings, are modeled with the theory of differential equations.

[@joeschmo6499]

almost said denumerator lol

[@garvSensei999]

from now on i hate mathematics

[@klipikareddy3250]

Thank you