Hyperbolic Functions - The Basics

In this video, I give the definitions of the hyperbolic functions, do a rough graph of three of the hyperbolic functions, evaluate a few of the functions at different values, and lastly I justify a couple of identities.

[patrickjmt]

glad i put it up then : )

in my experience, I do not run into hyperbolic functions much (i mean they do have useful applications) in a normal calculus class.

[patrickjmt]

@dvermilion not a new idea at all, but still a good one. i tried to get students to do this when i taught and they mostly had a fit and refused. so, instead of doing the interesting stuff, we had to do the basics.
another problem with the usa style is the sheer number of topics taught. i do not think everyone needs to know about roots of unity... instead, do a few topics, much more in depth so that people get a better grasp and appreciation for what is going on.

[bigfrug]

I just want you to know I'm an engineering major and you save my life a lot. And have been since I was probably 12. Thanks for all your great videos!!

[kawaii]

You have no idea how much you helped me finally understand this!!! I was so lost in class!!! Thank you!!

[teeheejohny]

wow this is so simple, my professor made it sound like rocket science and spent three hours explaining what hyperbolic functions are and i didnt get it. I watch your ten minute video and now it all makes sense. Thanks man!!

[joeyhardin]

To clarify: The method of using ((e^x)-(e^-x))/2 = sinh(x), is in radians, not degrees.

[wadexism]

why have i not thought about youtube help on math before?! OMG u make it soo easier for me to understand calculus than reading this damn textbook! lol im having finals next week but im sure ill grasp everything easily from u .. THANK YOU PATRICK! : )

[DarrellVermilion]

@patrickJMT i'll have to honestly admit that although I have tried on a number of occasions to read subject matter prior to coming to class, i always experienced diminishing returns on how much it helped me due to the book generally not doing a good job of explaining concepts. youtube has been an incredible resource to me in this way, and i generally watch your videos along with sal's before i even start homework. i think it's the medium that lends itself to learning in this way.

[patrickjmt]

they can be used to model a hanging wire, such as between two telephone poles

[glayo_]

I don't even need to learn maths to this degree, and I understood it nice and easily, so thank-you!

[roni]

Hey Patrick,

Great video. None of my first year university math classes covered these... until I ended up with an integral that evaluated to a hyperbolic sine while working on problems.

[renan]

Great explanation. Learning it now. P.S. you explain a way much than professors at university!

[aasarsak]

So helpful! The sinhx + coshx identity was the critical part of solving a diff. eq. problem I have been banging my head against the wall over all night. Thanks!!!! I even made a video in case someone else had the same problem.

[Hoehne]

These videos have taught better than my professors me calc 1-3, diff eq (ode), and hopefully pde when i have to take it, they are also a great review to for subjects I haven't seen for some time, thanks.

[MaxTechEngineering]

I greatly appreciate the clarity with which you explain out each of your actions as you work through the problems. Thank you!

[DashofDosh]

Thank you much!! I feel so much better about Calculus 2 now! :D

[Winfield]

very impressive, well explained at a great pace for learning. Props

[sulthanmubarok]

i'm first time watch this video, and i'm first time understand about mathematics engineering, thank a lot!!!

[joeyhardin]

Can we use a right angle triangle to work out these hyperbolic functions? If so, how? If not, why is it part of trigonometry?

[shaima]

a student in information system at college of computer science and you are saving my life :)