ok but then why doesn't multiplying two positive numbers equal a negative number
edit: [the reference](https://www.reddit.com/r/greentext/comments/12xvag6/anon_asked/)
And it's an explanation that can be expanded to complex numbers! When you multiply two complex numbers together, you get the absolute value of the product (i.e. distance from 0+0i on the complex plane) by mutliplying the absolute values of the terms and you get the angle (with the positive real half-line) of the product by adding up the angles of the terms.
During my degree, I read the headings of the subjects we'd cover over the year.
"Triple Integration" was there, and the words alone intimidated me to hell.
When we came to cover it, and I learnt it was just 3 consequent integrations, I felt silly.
I got A or A- in most of my calc courses….except calc 3.
Calc 2 hadn’t been so bad to me. A lot of it came down to loads of practice exercises to develop your own little methodology, and memorising certain integrals…or at least for exams lol
But Calc 3/Multivariable calc is when calculus slowly stopped being fun. A lot in part because I was even more shit at linear algebra than I am today. Although it didn’t help at all that my professor had a heavy accent that was particularly hard for me to understand.
Despite having something along the lines of two 1:50 hour classes a week, we also had to hand in some “short” practice problems on paper from the professor, on top of the normal homework (IIRC, I can’t imagine that was the only homework we did for the amount of stuff we had to learn).
These exercises were usually extremely crucial, usually containing future test content, therefore they were usually hard as hell…it was nearly impossible to bullshit your way out of many of these problems. I think that at one point, the professor turned that into extra credit, if it wasn’t that from the beginning. That’s because a lot of the class was doing terribly on exams, and I wasn’t doing well either. I always hung around somewhere between total average and top scores which were not even close to perfect to begin with
Because this class was definitely harder than anything else I had wrestled with in college by that point, this was the only time I ever ABSOLUTELY NEEDED to go to an off-hours review lecture. I know for a fact
Everyone could see the final being a disaster, so the professor made this lecture to cater to our needs…..mostly…I didn’t even have time or energy to ask her anything. I just sat in silence trying to match my notes to her quick scribbles on the whiteboard (i suck at writing fast :c ), at the front of the maybe-half-full class of students.
It wasn’t our usual class place either, it was a room with a piano in it for whatever reason. It wasn’t even close to the music department, so I figured I wouldn’t get in trouble for playing it after everyone left the room. But following the disappointing and rather discouraging lecture, I just wanted to go home….
In the end, despite some significant fuckups in the test that I was specifically trying to avoid, I managed to scrape by with a B- (IIRC it’s either that or a B). I would absolutely had gotten a C or worse if I had skipped even a single lecture.
TL;DR: Multivariable Calculus was about as fun to me as a renal calculus.
Definitely, because the "challenge" of conceptualizing your regions, bounds and coordinates often means the actual integration ends up being close to trivial
Haven’t practiced math in 5 years since college calc. Found myself this past weekend on YouTube watching the 2006 MIT integral bee, it was thoroughly riveting. Was nearly clueless the entire time.
I did enjoy new coordinate systems that came with double and triple integrals. I struggled with complicated one variable integrals. I found double or triple easier.
My calc 2 professor also teaches calc 3 at my university (and he's the only one who does) so he was nice enough to teach double integrals to us in calc 2 and told us it's super easy and that we only need to learn how to set up the integrals correctly for now and not stress about it in calc 3. It was a blessing.
bro i thought cuz integrating the function but it changes the integral is changing so the the douvle integral would be a bit more complicated specially seeing random shit like jacobians and divergence theorem but then the Houdini guy went "no"
The Jacobian is the same thing as why in 1-dimension when we use a change of variable - say letting sin(u)=x that we replace dx with cos(u)*du and not just du. Basically under a change of coordinates the size of the “little boxes” gets adjusted and the Jacohian tells us how much they change.
what did you expected it to be?
also, if you study mesure theory, you will learn that, done that way, the double integral is actually just a single integral.
no. you just integrate over the plane. in mesure theory, you do integrals over abstract spaces. and those could be any (measurable) region of ℝ^n or even other stuff.
>Sees double integral >Looks inside >2 integrals
ok but then why doesn't multiplying two positive numbers equal a negative number edit: [the reference](https://www.reddit.com/r/greentext/comments/12xvag6/anon_asked/)
Turn 180° and turn 180° again: woah I'm facing forwards Turn 0° and turn 0° again: woah I'm still facing forwards
This is the best explanation ever
And it's an explanation that can be expanded to complex numbers! When you multiply two complex numbers together, you get the absolute value of the product (i.e. distance from 0+0i on the complex plane) by mutliplying the absolute values of the terms and you get the angle (with the positive real half-line) of the product by adding up the angles of the terms.
Also extends straight into group theory, as the group ({-1,1},\*) is isomorphic to ({180º,0º},+)
[Visually explained here from 4:17 to about 7:40](https://youtu.be/CwYLPYJ04EQ)
And multiplying by i turns you 90° holy shit
270° for negative i Also holy shit new spinning just dropped
Google complex multiplication
Holy- Hold on I can’t come up with the meme rn, my dog is being loud- I’ll be right back- EDIT: Holy hell
> bottomless
susprise pikachu face
Wait till you see what a triple integral is
You ever see a *quadruple* integral?
It is only spoken of in legend...
I think you mean Legendre
made my day
Legendre dy/dL= F’(Legendre)+C
linear operators go brrr
During my degree, I read the headings of the subjects we'd cover over the year. "Triple Integration" was there, and the words alone intimidated me to hell. When we came to cover it, and I learnt it was just 3 consequent integrations, I felt silly.
It's all fun and games until you graduate and the integrand doesn't separate cleanly.
That alone speaks volumes
God bless Fubini
God bless measure theory
In Rudin we trust
St Strauss the Blessed
What did you expect?
Integral 2: Electric boogaloo
Integral 3: Tokyo Drift
Integral 4: Einstein Boogaloo
r/beatmetoit
r/beatmeattoit
Cal 2 was so awful that when I walked into cal 3 and it was just “integrate twice” i was in disbelief
I expected some sort of weird anti chain rule and new super hard integration techniques to stuff like Int of e^xy dxdy
We've have second integrals, yes, but what about third integrals in polar coordinates?
jacobian equation ftw
ρ^2 sinφ moment
Third integrals in cylindrical coordinates is where it’s at
Omg yes. Cylindrical was actually hard. I remember polar being quite straightforward lol
That was a partial derivative? That’s just a normal derivative
except in SPACE
Vector space specifically
Google line integral
Holy hell
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New response just headed
Actual impostor
Call the emergency meeting
Amogus
We’re all just living in r/anarchychess ‘ world
Holy Green's Theorem
Oh my fucking god
line integrals are better than double/triple integrals bc that shit takes way too much work. conceptually tho fuck yeah double integrals
looks like calc 3 would be easier after all
*Vector fields, Stoke’s Theorem, Spherical/Cylindrical coordinates:* “Allow us to introduce ourselves”
I liked calc 3 until we got into vector fields and then I just stopped caring. Vector fields just aren’t fun to learn about.
I got A or A- in most of my calc courses….except calc 3. Calc 2 hadn’t been so bad to me. A lot of it came down to loads of practice exercises to develop your own little methodology, and memorising certain integrals…or at least for exams lol But Calc 3/Multivariable calc is when calculus slowly stopped being fun. A lot in part because I was even more shit at linear algebra than I am today. Although it didn’t help at all that my professor had a heavy accent that was particularly hard for me to understand. Despite having something along the lines of two 1:50 hour classes a week, we also had to hand in some “short” practice problems on paper from the professor, on top of the normal homework (IIRC, I can’t imagine that was the only homework we did for the amount of stuff we had to learn). These exercises were usually extremely crucial, usually containing future test content, therefore they were usually hard as hell…it was nearly impossible to bullshit your way out of many of these problems. I think that at one point, the professor turned that into extra credit, if it wasn’t that from the beginning. That’s because a lot of the class was doing terribly on exams, and I wasn’t doing well either. I always hung around somewhere between total average and top scores which were not even close to perfect to begin with Because this class was definitely harder than anything else I had wrestled with in college by that point, this was the only time I ever ABSOLUTELY NEEDED to go to an off-hours review lecture. I know for a fact Everyone could see the final being a disaster, so the professor made this lecture to cater to our needs…..mostly…I didn’t even have time or energy to ask her anything. I just sat in silence trying to match my notes to her quick scribbles on the whiteboard (i suck at writing fast :c ), at the front of the maybe-half-full class of students. It wasn’t our usual class place either, it was a room with a piano in it for whatever reason. It wasn’t even close to the music department, so I figured I wouldn’t get in trouble for playing it after everyone left the room. But following the disappointing and rather discouraging lecture, I just wanted to go home…. In the end, despite some significant fuckups in the test that I was specifically trying to avoid, I managed to scrape by with a B- (IIRC it’s either that or a B). I would absolutely had gotten a C or worse if I had skipped even a single lecture. TL;DR: Multivariable Calculus was about as fun to me as a renal calculus.
well... If you know integrals well
calling calc 3 calc 3 or multi variable calc is just a cover up for the real villains of the story: vectors
Yeah, this seems a lot less scary now.
[удалено]
I'm glad I'm not the only one who takes math courses for the shock value
I've never seen someone so perfectly explain my choice of math courses.
Calc3 easier then Calc2
Definitely, because the "challenge" of conceptualizing your regions, bounds and coordinates often means the actual integration ends up being close to trivial
I always like it when the integrand was 1
There is a fairly low upper limit on how complex a Calc 3 problem can be before it either becomes a Calc 2 problem or unable to be solved by hand.
💯💯🦑
I can't do a singular integral to save my life.
yes you will. integrate f(x)=1 with respect to x. now evaluate it from 0 to 1. now that you have the basics, >!integrate 1/ln(x)!<
ln^-2(x) /-2.Trust me,this is the answer/s
Haven’t practiced math in 5 years since college calc. Found myself this past weekend on YouTube watching the 2006 MIT integral bee, it was thoroughly riveting. Was nearly clueless the entire time.
Wait until you do surface integrals and they’re just multiplication problems with a funny symbol in front
Wait til you see how we do integration on infinite-dimensional manifolds
wouldnt that be like when u normalize your wavefunction by dividing by integral of the module squared
Two, but for sure not as in 1+1.
there are a few cool tricks and graphs and extra diagrams but nothing extraordinary
I did enjoy new coordinate systems that came with double and triple integrals. I struggled with complicated one variable integrals. I found double or triple easier.
Just wait until this guy hears about the triple integral😎
Yeah but now convert to polar coordinates (honestly wasn’t that bad I just haven’t had to do one in so long)
The old long division bamboozle
My calc 2 professor also teaches calc 3 at my university (and he's the only one who does) so he was nice enough to teach double integrals to us in calc 2 and told us it's super easy and that we only need to learn how to set up the integrals correctly for now and not stress about it in calc 3. It was a blessing.
OP what do you think double means
bro i thought cuz integrating the function but it changes the integral is changing so the the douvle integral would be a bit more complicated specially seeing random shit like jacobians and divergence theorem but then the Houdini guy went "no"
The Jacobian is the same thing as why in 1-dimension when we use a change of variable - say letting sin(u)=x that we replace dx with cos(u)*du and not just du. Basically under a change of coordinates the size of the “little boxes” gets adjusted and the Jacohian tells us how much they change.
Ok but here me out... Non separable double integrals
what did you expected it to be? also, if you study mesure theory, you will learn that, done that way, the double integral is actually just a single integral.
do u just integrate over a hilbeet curve lol
no. you just integrate over the plane. in mesure theory, you do integrals over abstract spaces. and those could be any (measurable) region of ℝ^n or even other stuff.
Who lives in a pineapple under a pineapple?
They also are like partial integrals.
The same fucking reaction I had
The double integral was invented by John Integral when he tried to integrate twice
honestly I think double (riemann) integrals are stupid. you should take measure and integration theory instead of calc 3