Multivariable Calculus | Parameterized surfaces

We introduce the notion of a parameterized surface and give a few examples.
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[@giovannimariotte4993]

Honestrly I believe this is one of the best courses of multivariable calculus on the entire KZbin, thanks

[@SMD1999]

Parameterization of the cylinder doesn’t seem right to me. Looks like you had written in a radius of 2 instead of three like you originally had in the question

[@howardbaxter2514]

Thank you so much! I was struggling to understand my homework for my Differential Geometry class, and this video helped me so much with understanding parametrization and mapping sets.

[@sinus_hiphop]

finally someone explained this to me in a properly understandable manner. thanks a lot, Michael!

[@husseinshimal7567]

This is the best lecture I've ever watched so far

[@mehdisi9194]

It would be great if you could make a video about Riemannian surfaces in complex analysis. Thank you so much.

[@massivelooser3071]

Question: Are you going to do a series on differential geometry and tensor calculus once you are done with you multivariable calculus series?

[@MichaelPennMath]

My plan is to introduce differential forms and go far enough to see the real Stoke's Theorem and present the differential forms version of Maxwell's equations.

[@mehdisi9194]

@@MichaelPennMath That would be great.

[@duckymomo7935]

Is there any benefit to going any higher than R3? (Or R4, is thats mikowski Space time?) I mean except for specific cases like R10, R11 In string theory It really doesn’t seem necessary to over generalize when sufficient generalization should work Just my opinion

[@thomasazeredo9632]

When you discuss a surface which is the graph of a function of three variables, aren't you in R^4? No need to think of "Minkowski" space time. When an agricultural economist considers the cost of production of wheat per farming acre in Iowa [to be directly down to earth] based on factors such as rainfall, nitrogen content in the soil, labor, gas price, upkeep of machinery, for example,isn't that a function of 5 variables? So the graph describes a surface in R^6? Applications of calculus in spaces of many [finite] dimensions will, in practice, be confronted by indefinitely many spaces of different dimensions. .... or did I misunderstand your point?

[@duckymomo7935]

Thomas Azeredo makes sense In economics, you can even have R365 just for days in a year