Fuck, I wish I had this when I took my Uni calculus class. I would have much rather learned the formulas instead of programing them into my calculator. I didn't learn anything in my class instead of plugging and chugging.
@Bleachnarutoawesome "Easy, learn integration, then you will realize how easy differentiation is." This video implies that derivatives are hard. You are saying it is easy in comparison to integration, therefore you are saying that integration is hard. Maybe thats not what you meant, but it sure seems like you did D:
@MMOseth Since we have posts by a couple of cocky undergrads who seem unwilling to admit that integration is difficult, let me say it instead: Integration is difficult. (By integration I mean the act of expressing an indefinite integral in terms of elementary functions.)
Differentiation is easy because of the product rule and chain rule which lets you compute the derivative of any composition as long as you know the derivative of the individual functions. No corresponding rules exist for integration. In fact anyone claiming that integration is easy has probably a) only practiced on selected "easy" instances, and b) not really understood the problem of integration.
To take a couple of examples: What is the integral of exp(-x^2)? What is the integral of 1/ln(x)?
You can try to "compute the integrals", but you will not succeed. The reason is that the integrals above are non-elementary, i.e. *cannot* be expressed using only elementary functions. To prove this fact you use differential algebra and Liouville's theorem (not the one from complex analysis).
What is the integral of exp(x^2)(2x^3-2x^2-1)/(x-1)^2?
Despite looking more complicated, one can show that it is exp(x^2)x/(x-1). This is done by considering towers of differential field extensions. As long as the extensions are transcendental, the algorithm requires relatively little prerequisites, but for algebraic extensions you need to know differential geometry. Further pursuing integration and differential equations leads to differential Galois theory.
@EudoxusOfCnidus Thats like saying "learn how to divide and multiplication will be easy." Its no different in difficulty. All you have to do is remember some tricks and bam, you know calculus.
@MMOseth Integration is definitely more difficult than differentiation. (One could argue that division is more difficult than multiplication, but the difference is so small that I prefer not to.) The problem with integration is that your "tricks" don't really work in general. If you don't believe me, please try integrating exp(x^2) using the ordinary methods from calculus.
@EudoxusOfCnidus You dont get it. Im saying you learn new tricks for integration (integration is part of calculus by the way). But, for the most part, its just that, learning a a few tricks to remember. Difficulty is relative. To me, integration is easy, and learning that was just as easy (or difficult) as learning differentiation. Anyway, all im sayin is people learn things differently, and i guess it was just harder for you than it was for me. Stop bitchin, stop actin like you know everything.
I think you should upload more videos like this if you can :) This was seriously fun to watch, and I'm actually going to save this song in my favorites and listen to it until I remember it all
Thanks so much for the promotion of my video. I look forward to introducing you to Berry's campus when you begin looking at colleges. Perhaps you can appear in a future production!
@Bleachnarutoawesome It seems bad at calc I, but triple integrals, line integrals, surface integrals, and everything else in calc III is kinda confusing lol...I gotta retake it..enjoy calc I, and make sure that you understand everything!!!
@Tkdkid9 Calculus is easy. Real mathematicians do "Analysis" which is more rigorous... But that's fine too. Now abstract algebra, and algebraic topology. That's the real stuff.
Now, that's a awesome teacher. Wish i had one of those when i went to school. I might have actually learned something. He looks like the kinda dude that try to find solutions on how to help a student that really needs it. ^___^
I have absolutely NO IDEA what you're talking about, Eric, but it's still a VERY clever song, and a cute video. I'm sure that to Math Majors this is hysterical, but its all Greek to me, and I'm a GDI, and an MFA candidate to boot... Your students must really get a lot from your classes. If I'd had teachers like you as an undergrad, I might have actually enjoyed the math classes... (--Your old Bethany Room-mate)
I play ragtime.. and I'm on the chain rule right now. This video needs more views!
PlaceBoInternational 3 weeks ago
1:07 for a massive troll face on the girl.
MikelZseo 1 month ago
Comment removed
MikelZseo 1 month ago
Stay Frosty, Dr McDowell
ToddSQL 4 months ago
jazz hands!
cllewis1 4 months ago
so glad i was able to learn from dr. mcdowell at least once while i've been here at berry!
CHSAT08 4 months ago
Fuck, I wish I had this when I took my Uni calculus class. I would have much rather learned the formulas instead of programing them into my calculator. I didn't learn anything in my class instead of plugging and chugging.
AozoraFai 4 months ago
This has been flagged as spam show
@Bleachnarutoawesome "Easy, learn integration, then you will realize how easy differentiation is." This video implies that derivatives are hard. You are saying it is easy in comparison to integration, therefore you are saying that integration is hard. Maybe thats not what you meant, but it sure seems like you did D:
MMOseth 5 months ago
@Bleachnarutoawesome integration is easy too. In fact, calculus itself is easy as fuck, its just the algebra that comes after that sucks.
MMOseth 5 months ago
@MMOseth Since we have posts by a couple of cocky undergrads who seem unwilling to admit that integration is difficult, let me say it instead: Integration is difficult. (By integration I mean the act of expressing an indefinite integral in terms of elementary functions.)
EudoxusOfCnidus 4 months ago
@EudoxusOfCnidus cont.
Differentiation is easy because of the product rule and chain rule which lets you compute the derivative of any composition as long as you know the derivative of the individual functions. No corresponding rules exist for integration. In fact anyone claiming that integration is easy has probably a) only practiced on selected "easy" instances, and b) not really understood the problem of integration.
EudoxusOfCnidus 4 months ago
@EudoxusOfCnidus cont.
To take a couple of examples: What is the integral of exp(-x^2)? What is the integral of 1/ln(x)?
You can try to "compute the integrals", but you will not succeed. The reason is that the integrals above are non-elementary, i.e. *cannot* be expressed using only elementary functions. To prove this fact you use differential algebra and Liouville's theorem (not the one from complex analysis).
EudoxusOfCnidus 4 months ago
@EudoxusOfCnidus cont.
What is the integral of exp(x^2)(2x^3-2x^2-1)/(x-1)^2?
Despite looking more complicated, one can show that it is exp(x^2)x/(x-1). This is done by considering towers of differential field extensions. As long as the extensions are transcendental, the algorithm requires relatively little prerequisites, but for algebraic extensions you need to know differential geometry. Further pursuing integration and differential equations leads to differential Galois theory.
EudoxusOfCnidus 4 months ago
@EudoxusOfCnidus Correction of prev. post: Obviously one uses *algebraic* geometry for the algebraic extensions :-)
EudoxusOfCnidus 3 months ago
@EudoxusOfCnidus Thats like saying "learn how to divide and multiplication will be easy." Its no different in difficulty. All you have to do is remember some tricks and bam, you know calculus.
MMOseth 3 months ago
@MMOseth Integration is definitely more difficult than differentiation. (One could argue that division is more difficult than multiplication, but the difference is so small that I prefer not to.) The problem with integration is that your "tricks" don't really work in general. If you don't believe me, please try integrating exp(x^2) using the ordinary methods from calculus.
EudoxusOfCnidus 3 months ago
@EudoxusOfCnidus You dont get it. Im saying you learn new tricks for integration (integration is part of calculus by the way). But, for the most part, its just that, learning a a few tricks to remember. Difficulty is relative. To me, integration is easy, and learning that was just as easy (or difficult) as learning differentiation. Anyway, all im sayin is people learn things differently, and i guess it was just harder for you than it was for me. Stop bitchin, stop actin like you know everything.
MMOseth 3 months ago
this just made me more fearful of derivatives O.o
iJOKEx 6 months ago
I think you should upload more videos like this if you can :) This was seriously fun to watch, and I'm actually going to save this song in my favorites and listen to it until I remember it all
jennys2151 8 months ago
@jennys2151 Dear Jennys2151:
Thanks so much for the promotion of my video. I look forward to introducing you to Berry's campus when you begin looking at colleges. Perhaps you can appear in a future production!
drmathman 7 months ago
muito bom!!!!
mtomazza 10 months ago
2:28 Oops! Amazing video though.
DavidSpencer6174 10 months ago
@Bleachnarutoawesome It seems bad at calc I, but triple integrals, line integrals, surface integrals, and everything else in calc III is kinda confusing lol...I gotta retake it..enjoy calc I, and make sure that you understand everything!!!
Tkdkid9 10 months ago
@Tkdkid9 Calculus is easy. Real mathematicians do "Analysis" which is more rigorous... But that's fine too. Now abstract algebra, and algebraic topology. That's the real stuff.
rlinfinity 9 months ago
@Bleachnarutoawesome So true...Calc II and III makes calc I look like a piece of cake lol
Tkdkid9 10 months ago
Well done.
10inchserratedblade 10 months ago
Now, that's a awesome teacher. Wish i had one of those when i went to school. I might have actually learned something. He looks like the kinda dude that try to find solutions on how to help a student that really needs it. ^___^
T3n50r 11 months ago 6
fogers and gofers! love it!
1991nadia1991 11 months ago
Awesome
calvinhobbesliker2 1 year ago
omg where was this last semester when i was in differential??!?
vainglorygirl 1 year ago
awesome!!
LallaRellaH 1 year ago
Dr. McDowell crowdsurfs! lol
trackstarlol 1 year ago
I shall watch this once again when I have to take math... I have a feeling I will be singing this a lot through out that semester.
felipeleoanm 1 year ago
I see me!
-Danny
iamracecar 1 year ago
I have absolutely NO IDEA what you're talking about, Eric, but it's still a VERY clever song, and a cute video. I'm sure that to Math Majors this is hysterical, but its all Greek to me, and I'm a GDI, and an MFA candidate to boot... Your students must really get a lot from your classes. If I'd had teachers like you as an undergrad, I might have actually enjoyed the math classes... (--Your old Bethany Room-mate)
stereodreamer23 1 year ago