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.
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
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.
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
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?
Honestrly I believe this is one of the best courses of multivariable calculus on the entire UA-cam, thanks
finally someone explained this to me in a properly understandable manner. thanks a lot, Michael!
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.
This is the best lecture I've ever watched so far
It would be great if you could make a video about Riemannian surfaces in complex analysis. Thank you so much.
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
Question: Are you going to do a series on differential geometry and tensor calculus once you are done with you multivariable calculus series?
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.
@@MichaelPennMath That would be great.
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
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?
Thomas Azeredo
makes sense
In economics, you can even have R365 just for days in a year