Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses

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We've learned about trigonometric functions, which relate to the unit circle. So what are hyperbolic functions? Why, those relate to the hyperbola of course! They are a little strange, but once we go through some details they will start to make sense a little bit.

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Ive taken calc 1, 2, 3, linear algebra, intro to differential equations, and am now in complex vector analysis and somehow avoided learning about hyperbolic functions. This was great explanation and just what I needed for this class. Thank you :)

Dina-heuc

Professor Dave, you continue to deliver on the kicks in the discovery.

Learning that Hyperbolic geometry is literally geometry with Hyperbolas has warmed my soul

hareecionelson

Great video Dave. Enjoy all your uploaded material. You truly have mastered the art of distilling a topic to it bare essence. Your fan following is very lucky to have you. Just missed one small point though in this particular video. You forgot to explicitly describe the relationship between these trigonometric hyperbolic functions to an actual graphical hyperbola. That I think would have made the video just a tiny bit more complete.

Tom-spgy

It was the best . I liked your video very much. I was so confused about these h functions but your amazing video helped me a lot. Thank you very much sir.

gursharansingh

I have been roaming for so long
But finally i have found him 🙏
His name is Professor Dave

ferkahmathiasgyinantwi

Brilliant. Truly short and poignant, thank you for making this and uploading it.

Cristian-ieet

I Had a calculus class this morning about this exact hyperbolic functions, and it took 90minuts, and professor dave finished it in 7 minutes.

Thank you professor dave

sobhansabbagh

Might have mentioned that y=cosh x makes a catenary.

comicrelief

I never learned hyperbolic functions in Calc 2, this is a great help in calc 3

andrewmaksimovich

Wish you were my face to face teacher!!

yiannisserpico

The video I was searching for.., is Finally found👍. Very well explained

bhuvanachandrika

The graph of the system
y = (1/2)e^x
y = -(1/2)e^x
is clearly not a hyperbola. On a hyperbola with no vertical asymptotes, the limit of dy/dx as x approaches plus or minus infinity should be finite (it should approach a line). For y = (1/2)e^x, dy/dx = (1/2)e^x which increases without bound as x approaches infinity (the graph does not approach a line).

jello