Does anyone have a pdf with buttloads of solved contour integrals? Maybe also the preliminary exercises that go with it (series expansions, maybe some parametric stuff, ... ), though less important.
Really need to get comfortable with it...
Man, I missed the class that explained derivatives and now I'm very confused. This won't end well.
[editline]6th November 2014[/editline]
i think i've got it figured out, though
the only thing that's still confusing is that the book explains derivatives as being calculated with the limit of h->0 and the equation (this will be obnoxious to write) being somethng like limh->0 (f(x+h)-f(x))/h
but why is that necessary when it seems like you always calculate them with h->0
like if i wanted to find the derivative of somethng like a^3 (which isn't hard with power rules or whatever) I'd have to go through the trouble of calculating it and canceling out h but i don't understand why h is necessary
perhaps there's just some weird property of a derivative that i'm missing that makes it all make sense
If you're going to be rigorous about it, then you can't use the power rule until you've proven it using the h->0 definition. After a certain point the class will have proven all these shortcuts and rules using the definition and you won't need to use it to actually calculate a derivative.
[editline]6th November 2014[/editline]
Also, if you're not dealing with a polynomial, calculating a derivative using the definition is less straightforward (though not impossible). For example, [url=http://www.themathpage.com/acalc/exponential.htm#expon]the exponential function[/url].
it's not really that bad, it's only annoying dealing with fractions and shit
also sin and cos, i always have trouble getting derivatives involving them which is something i should probably fix since those seem important
[QUOTE=Remedial Math;46429491]it's not really that bad, it's only annoying dealing with fractions and shit
also sin and cos, i always have trouble getting derivatives involving them which is something i should probably fix since those seem important[/QUOTE]
I doubt you'd be expected to calculate derivatives in general using their definition. You might get asked the odd question in order to test your knowledge of it but throughout your maths education, you won't be expected to implement that everytime you need to calculate a derivative.
[QUOTE=Remedial Math;46427783]Man, I missed the class that explained derivatives and now I'm very confused. This won't end well.
[editline]6th November 2014[/editline]
i think i've got it figured out, though
the only thing that's still confusing is that the book explains derivatives as being calculated with the limit of h->0 and the equation (this will be obnoxious to write) being somethng like limh->0 (f(x+h)-f(x))/h
but why is that necessary when it seems like you always calculate them with h->0
like if i wanted to find the derivative of somethng like a^3 (which isn't hard with power rules or whatever) I'd have to go through the trouble of calculating it and canceling out h but i don't understand why h is necessary
perhaps there's just some weird property of a derivative that i'm missing that makes it all make sense[/QUOTE]
Not quite sure why h wouldn't be necessary?
[f(x+h) - f(x)]/h is just a the formula for the slope of a line between between the image of the point x and the image of a point h units away from x. Taking h -> 0 amounts to finding the slope "at x." If you're somehow not using h or something similar, you're moving away from this "slope of a line" interpretation so you're computing a quantity with a completely different interpretation.
We had this question in our homework, and I missed the lecture on limits :v:
[img]http://latex.codecogs.com/gif.latex?%5Clim_%7Bx%20%5Cto%20%5Cinfty%20%7D%20%5Cleft%28%5Cfrac%7Bx+1%7D%7Bx%5E2+6x%7D%5Cexp%5Cleft%28%5Cfrac%7Bx%5E2%7D%7B1+x%5E2%7D%28%5Cln%28x%29%20+%202%29%5Cright%29%5Cright%29[/img]
I spent over two hours on it (it was very late, I was sleepy...)
oh yeah, pebkac is right
You can't just handwave away all the constants, especially when they're in an exponent. Doing that's gonna bite you in the ass cause the actual answer is e^2. You have to be a bit more rigorous.
Hint: Start by factorizing that exponential so you can break the expression down into a product of two limits.
Yeah the answer is e^2, I did pretty much what pebkac said
It took me ages because I had no idea how to approach it... my main mistakes were just fluffing my my indices laws.
I'm studying CS, but I like my math classes way more than my CS classes. I'm still really interested in Computer Science, but I'm more interested in ACTUAL Computer science, not just programming. I'm afraid, however, if I take a lot of higher math classes later on in college, that I'll have missed all the programming and practical skill classes that would give me marketable skills. Is general knowledge of math a desirable skill in the CS field? And are there commercial uses for theoretical computer science? I'm still learning programming, but moreso on my own terms since my CSC200 classes aren't exactly teaching me anything new. I'm planning on taking discrete math next semester and I want to see if they have a number theory class as well.
On a side note, I picked up "The USSR Olympiad Problem Book" from barnes and noble. it's got 300-ish difficult problems from an old soviet national math competition. the first 60-ish pages are the problems. the next 340 pages are the solutions.
So, I'm learning calculus with this book my dad found in a trash can, but I'm stuck in a little problem:
[t]http://i.imgur.com/bL2f6S9.jpg[/t]
problem 29
[QUOTE=proboardslol;46454123]I'm studying CS, but I like my math classes way more than my CS classes. I'm still really interested in Computer Science, but I'm more interested in ACTUAL Computer science, not just programming. I'm afraid, however, if I take a lot of higher math classes later on in college, that I'll have missed all the programming and practical skill classes that would give me marketable skills. Is general knowledge of math a desirable skill in the CS field? And are there commercial uses for theoretical computer science? I'm still learning programming, but moreso on my own terms since my CSC200 classes aren't exactly teaching me anything new. I'm planning on taking discrete math next semester and I want to see if they have a number theory class as well.
On a side note, I picked up "The USSR Olympiad Problem Book" from barnes and noble. it's got 300-ish difficult problems from an old soviet national math competition. the first 60-ish pages are the problems. the next 340 pages are the solutions.[/QUOTE]
Personally - depending on if your school will allow you to or not; mine didn't, but a lot of state unis do - I would consider doing a CS and Mathematics Dual Major. I did that for my Associates in Mathematics and Physics, which we could dual in, but not in CS and Math because; Community College.
Also, related, I think Mathematical Structures is going to be one of your strongest classes that you'll enjoy the most then. That was easily my favorite class I took for my degree, even if I haven't used hardly anything I learned of it in two years.
[QUOTE=Cosa8888;46458219]So, I'm learning calculus with this book my dad found in a trash can, but I'm stuck in a little problem:
[t]http://i.imgur.com/bL2f6S9.jpg[/t]
problem 29[/QUOTE]
I'm sure that I over-thought this but here's a try:
[IMG]http://postimg.com/175000/snells-174582.jpg[/IMG]
I did it today, following a much simplier aproach:
[t]http://i.imgur.com/luzlJaf.jpg[/t]
Excuse the shitty handwriting and organization.
On another note, my math teacher told me that I can enter some weird maths contest. Basically, I have to solve a big ass problem about some Jamaican dude coming to Chile to see the Copa America. He wants to see specific teams, visit some places all around the country, and every thing he does has a "value", and a cost; for example, going to a game has a value of 20 points and it's worth about 20000 pesos, wich is substracted from the dude's budget. And I have to count the kilometers he travels because he spends 50 $/km on fuel. My job is to find a path for the weird Jamaican dude wich nets me the most points, with some extra conditions and time, like going to a game on a determined date and city, all while staying in his shitty budget of 1400000 pesos/ 700 dollars.
It looks like a looong problem. I have until the 28th to solve it, along with my girlfriend.
I was thinking that maybe some of you guys are willing to give us a hand.
[QUOTE=Cosa8888;46458219]So, I'm learning calculus with this book my dad found in a trash can, but I'm stuck in a little problem:
[t]http://i.imgur.com/bL2f6S9.jpg[/t]
problem 29[/QUOTE]
The neatest (imo) way to solve this doesn't use calculus at all*:
[img]https://dl.dropboxusercontent.com/u/4081470/first.png[/img]
We can phrase the question as: What position of C minimises |AC| + |CB|?
To help us, we add the reflection of B, say, B'
[img]https://dl.dropboxusercontent.com/u/4081470/reflected.png[/img]
It's clear (I hope) that |CB| = |CB'|, thus we can equivalently state it as:
What position of C minimises |AC| + |CB'|?
But this is obvious - the answer is a straight line! (Any other position forms a triangle, and the sum of any two sides is longer than the other)
When it's a straight line, it's trivial to deduce angle of incidence = angle of reflection.
*Maybe you were intended to use calculus, but any decent maths teacher should appreciate that a proof is a proof, and an elegant proof is even better...
I saw [URL="http://en.wikipedia.org/wiki/Yitang_Zhang"]Tom[/URL] at the engineering library at UNH relaxing with his shoes off in one of the sofas. He was a lecturer in one of my classes before his proof came to light.
Might not belong here, but meh.
[editline]12th November 2014[/editline]
[QUOTE=proboardslol;46454123]I'm studying CS, but I like my math classes way more than my CS classes. I'm still really interested in Computer Science, but I'm more interested in ACTUAL Computer science, not just programming. I'm afraid, however, if I take a lot of higher math classes later on in college, that I'll have missed all the programming and practical skill classes that would give me marketable skills. Is general knowledge of math a desirable skill in the CS field? And are there commercial uses for theoretical computer science? I'm still learning programming, but moreso on my own terms since my CSC200 classes aren't exactly teaching me anything new. I'm planning on taking discrete math next semester and I want to see if they have a number theory class as well.
On a side note, I picked up "The USSR Olympiad Problem Book" from barnes and noble. it's got 300-ish difficult problems from an old soviet national math competition. the first 60-ish pages are the problems. the next 340 pages are the solutions.[/QUOTE]
I'm currently going for an Applied Mathematics degree specific to computation. I do know that knowing a bit in mathematics can be pretty useful.
I haven't taken any 200-level classes in CS; I just jumped to 400 and 500. May I ask what languages you're using?
[QUOTE=Joey90;46470120]The neatest (imo) way to solve this doesn't use calculus at all*:[/QUOTE]
Yeah but then you get the raging math stiffy that comes with using the Euler-Lagrange equation.
[I]so elegant[/I]
Any folks here taken a 'history of math' course in college and have something to say about it? I'm able to take it to fulfill a GE next quarter and am considering it.
Looks like Grothendieck has died :C
[url]http://www.liberation.fr/sciences/2014/11/13/alexandre-grothendieck-ou-la-mort-d-un-genie-qui-voulait-se-faire-oublier_1142614?xtor=rss-450[/url]
It's weird, I was just reading about his life and work earlier today, and reading a little bit about schemes before I heard.
[QUOTE=danjee;46477675]Any folks here taken a 'history of math' course in college and have something to say about it? I'm able to take it to fulfill a GE next quarter and am considering it.[/QUOTE]
Easy as fuck. But only because of the professor.
The most difficult part was converting the ancient works of Euclid, Pythagoras, and those guys, and converting their ancient lingo to the more mathematical forms.
[editline]13th November 2014[/editline]
The professor took us out for ice cream on the last day.
So what's the gist of the course (lectures, assignments, exams)? The description on my class search is pretty scant..
[QUOTE=nerdster409;46474602]I saw [URL="http://en.wikipedia.org/wiki/Yitang_Zhang"]Tom[/URL] at the engineering library at UNH relaxing with his shoes off in one of the sofas. He was a lecturer in one of my classes before his proof came to light.
Might not belong here, but meh.
[editline]12th November 2014[/editline]
I'm currently going for an Applied Mathematics degree specific to computation. I do know that knowing a bit in mathematics can be pretty useful.
I haven't taken any 200-level classes in CS; I just jumped to 400 and 500. May I ask what languages you're using?[/QUOTE]
C/C++
[QUOTE=JohnnyMo1;46483052]Looks like Grothendieck has died :C
[url]http://www.liberation.fr/sciences/2014/11/13/alexandre-grothendieck-ou-la-mort-d-un-genie-qui-voulait-se-faire-oublier_1142614?xtor=rss-450[/url]
It's weird, I was just reading about his life and work earlier today, and reading a little bit about schemes before I heard.[/QUOTE]
What did he do? In English please :).
Also hello, one question!
Is it possible to use quaternions not for rotations, but translations and scalling of coordinate systems (instead of matrices?)
[QUOTE=proboardslol;46485027]C/C++[/QUOTE]
I don't know the math requirements for your degree, but some math education, including knowledge of matrices and their operations, will be useful.
I swear to god, this book is trying to kill me:
[t]http://i.imgur.com/sVrHu4a.jpg[/t]
All I got is Pythagoras but that doesn't help at all.
Anyone willing to give me a hand?
[editline]14th November 2014[/editline]
Oh, and it's problem 22
[QUOTE=proboardslol;46454123]I'm studying CS, but I like my math classes way more than my CS classes. I'm still really interested in Computer Science, but I'm more interested in ACTUAL Computer science, not just programming. I'm afraid, however, if I take a lot of higher math classes later on in college, that I'll have missed all the programming and practical skill classes that would give me marketable skills. Is general knowledge of math a desirable skill in the CS field? And are there commercial uses for theoretical computer science? I'm still learning programming, but moreso on my own terms since my CSC200 classes aren't exactly teaching me anything new. I'm planning on taking discrete math next semester and I want to see if they have a number theory class as well.
On a side note, I picked up "The USSR Olympiad Problem Book" from barnes and noble. it's got 300-ish difficult problems from an old soviet national math competition. the first 60-ish pages are the problems. the next 340 pages are the solutions.[/QUOTE]
Typically, there are 3rd and 4th year computer sicence courses on numerical methods, where you're dealing with problems where you're required to write a program to solving matrices or differential equations using numerical methods instead of symbol manipulation. A lot of other mathematical topics are typically covered in these courses as well, such interpolation and root of equations in these courses. You may wanna take a look into those classes when you're in your 3rd year.
[editline]14th November 2014[/editline]
Also consider applying for a math minor if you really enjoy higher math. Math and CS goes together bread and butter.
[QUOTE=Cosa8888;46490900]I swear to god, this book is trying to kill me:
[t]http://i.imgur.com/sVrHu4a.jpg[/t]
All I got is Pythagoras but that doesn't help at all.
Anyone willing to give me a hand?
[editline]14th November 2014[/editline]
Oh, and it's problem 22[/QUOTE]
Unless I'm missing something, this is just basic algebraic physics. To find vertical velocity, you just do Pythagorean as you said, with 500 being horizontal velocity and 700 being actual velocity. The way b is worded doesn't make sense to me, but my best guess would be Pythagorean again, but with 2 as horizontal and 4 as the hypotenuse.
[QUOTE=WastedJamacan;46494453] The way b is worded doesn't make sense to me, but my best guess would be Pythagorean again, but with 2 as horizontal and 4 as the hypotenuse.[/QUOTE]
disdainforplebs.jpg
I sense another Euler-Lagrange equation coming on!
[QUOTE=PopLot;46494612]disdainforplebs.jpg
I sense another Euler-Lagrange equation coming on![/QUOTE]
Oh wait i think i understand the problem now. Literally just misread the question. the second plane intercepts the first's [I]course[/I], not the plane itself.
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