Read the damned book. I mean sit down and READ it, page by page, picture by picture, not advancing until you understand everything, every figure, and every equation. You ALSO need to practice, just raw practice of doing problems. Most people just do one or the other(read or practice)
Limed. But you need to understand that mathematics textbooks are SO different from regular textbooks. The information density ends up being pretty high in a lot of cases, so it's slow going. And it's a much more thoughtful process--you need to 'get it' instead of just blasting through. This can help a lot, though--you're sitting down and putting in a lot of conceptual thought, which lays a foundation for doing problems AND of course still helps you understand the concepts.
MIT's open courseware has a ton of practice exams and problems you can try out. I find the best way to get good is practice until you are fast enough to finish the test early so you can check over your work and find your mistakes.
He is probably talking about Integration with limits at infinity. U substitution is pretty well covered in Calc I, generally.
Ahh okay.
Bah, sorry for the late reply. Yeah Improper Integration is the ones that have them at infinity. Also, you have to find the ones that are either convergent/divergent at whatever number.
The ones with infinity seem easy, just sub the infinite symbol for "t" and then solve down for t. But I can't ever picture the convergent/divergent ones.
I'll post an example either today or tomorrow (crazy busy today for some reason).
Haha, it's funny you say that. My instructor explains (every day) that he doesn't care for "understanding" the material, it's more about memorization than anything. He tells us to memorize it without actually explaining anything, which is what I started to try and do. Obviously failing, of course.
This is wrong. Your professor is an idiot. Math is all about understanding a concept and then building on that concept to reach some more interesting conclusion.
As to your specific problem and how to study for math, obviously doing problems is the best method. But the setting you want to do problems depends on the person. For some people study groups are really good, you get to bounce ideas off each other and see what actually works. Others need to be alone. Personally I combined the group work up through AP Calc in high school and then for college courses, when I was really struggling, I just ignored it for a while and my subconscious frequently figured it out. I don't recommend that method obviously, just telling you what I did.
A lot of times, a tutor can be really helpful. I tutored for the math department at the University of Michigan while I was an undergrad for four years. And if you find the right one, they can do a really good job (or at least, I'd assume that's why people kept coming back to me :P).
Now you mentioned you were struggling with partial fractions, for example. They're tricky at first but if you think about it in terms of something simpler that you know how to do, it's not too difficult.
Here's a (simple) example:
You want to integrate something like 1/(x-3)(x+4) (generally speaking, a polynomial in the denominator which can be factored into linear terms).
Now obviously we don't have a rule for that, and something like u substitution doesn't work.
So what do we do?
Let's consider a simple concept from waaaay back in your math career. Least common denominators!
Obviously you know how to do something 1/2 + 1/3 = 5/6. 1/2= 3/6 and 1/3= 2/6 and then add, woo.
So logically 1/(x-3)(x+4) should be equal to something/(x-3) + something else/(x+4), right? And if we have those, those are easily integrated! So set up the equation:
1/(x-3)(x+4)=A/(x-3) + B/(x+4)
Next step is that fractions are evil and should be destroyed at all costs to we multiply both sides by (x-3)(x+4) and get:
1=A(x+4)+B(x-3)
Now we have two unknowns we want to solve for (A and but only one equation. However, this equation has to be true for all values of x! So we can pick two specific values of x and solve for A and B from the two resulting equations. In our case, the two most convenient values of x are -4 and 3 and we get that
A=1/7 and B=-1/7.
So then to finally answer the question:
int(1/(x-3)(x+4))
=int(1/(7(x-3)) - 1/(7(x+4)))
=(1/7)ln(abs(x-3))-(1/7)ln(abs(x+4)) + C
So that's partial fractions and why it works. The other case is that you have something like (x^2 + 4) in the denominator, which obviously can't be factored. If that's the case, instead of having the numerator above it being a constant, it's a linear polynomial. (Ax +
Like: 1/(x^2 + 4)(x-3) = (Ax + /(x^2+4) + C/(x-3) for example. The algebra is more time consuming, but otherwise the process is the same.
So:
1) Nothing you can do but partial fractions
2) Factor the denominator
3) Separate the denominator into its factors with variables in the numerators, set this equal to the original integrand.
3) Destroy the fractions!
4) Pick values of x (arbitrary, though frequently particular values will make your life easier (0, 1, -1 are good if you have non-linear terms. If you have linear terms pick values of x that make the linear term 0 like I did above in picking 3 and -4)
5) Solve for the variables that were in your numerator
6) Rewrite your integrand
7) Integrate with methods you already know
8) Don't forget your + C!
Sorry for the length on this, but that's my lesson on partial fractions.
enlightenedbum on
Self-righteousness is incompatible with coalition building.
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Big DookieSmells great!Houston, TXRegistered Userregular
edited March 2008
Man, I hated Partial Fractions when I first started learning about them in Calc II. Differential Equations made me love them though. For me, it was one of those concepts that I just could not wrap my mind around, until one day it finally clicked with me and I could do them with no problem. Many things in Math seem to be like that. Just think about them long enough, even if you have no idea what you're doing, and eventually it will be like a switch going off in your head and you'll understand it.
Personally, in my degree (EE) so far, I've used partial fraction expansion more than just about any of the other concepts from Calc II. I still have a year left, so that may change, but they've been incredibly useful when analyzing circuits in the s domain. Of course, the lesson is that you will actually use most of this stuff at some point. I would imagine that, for CS, Sequences and Series will become very useful for you later on.
Man, I hated Partial Fractions when I first started learning about them in Calc II. Differential Equations made me love them though. For me, it was one of those concepts that I just could not wrap my mind around, until one day it finally clicked with me and I could do them with no problem. Many things in Math seem to be like that. Just think about them long enough, even if you have no idea what you're doing, and eventually it will be like a switch going off in your head and you'll understand it.
Personally, in my degree (EE) so far, I've used partial fraction expansion more than just about any of the other concepts from Calc II. I still have a year left, so that may change, but they've been incredibly useful when analyzing circuits in the s domain. Of course, the lesson is that you will actually use most of this stuff at some point. I would imagine that, for CS, Sequences and Series will become very useful for you later on.
I would agree in general. I can't really speak to the usefulness of the math, since I majored in, um, math so screw application, theory's where it's at, man!
But yeah, a lot of times math doesn't make sense and then it just clicks once you've done some number of problems or something fires in your brain. Keep doing problems, ask a friend who's good to help out, etc.
enlightenedbum on
Self-righteousness is incompatible with coalition building.
I got into a situation like this with Calc III, where I would have basically had to get a perfect on the final in order to pass the class. I ended up damn near having a nervous breakdown during the final and getting a 32%. The next semester, I got a tutor and spent a bit more time studying it, and I ended up with an A- overall.
My best advice if you're too far in the hole right now is to drop the class, study your ass off, get a tutor next semester and try again. The added pressure of having to perform above average in a class you're already not doing well in can lead to fucking it up regardless. Unless you're racing to get your degree or you're bound to a tight departmental schedule, retaking a class shouldn't be a big deal. You'll have the benefit of learning the material twice, and having already picked up the basics you'll be in a better position to understand the material as opposed to just learning the steps.
If it's too late to drop the class without the 'W' on your record, I say just fight it out. Don't kill yourself studying, but make a conscious effort to put down your pencil and just listen to what the prof is saying. You just need to get a groundwork for what's going on, provided you have to retake the class again. That makes it so that when you do take the class again, you'll be relearning what you already know from the first run through the class.
When I wake up tomorrow morning and that paragraph makes any sense at all, I'm going to be astonished.
Notes have never really helped me in a Math class. What I do is go through each chapter and more or less outline it, writing down equations and rules and whatever else I feel like I need to study. Then I go through and do the homeworks again, then finally end on practice exams.
I do this same process for pretty much every math intensive course I take.
And don't sweat Calc II too much, it is definitely the hardest one.
I also suck at studying for math. I managed to do well in Calc I, but Calc II was a swift kick in the nuts.
Just work the problems over and over until you recognize patterns etc. For me (I'm strange) it helps to set up problems PHYSICALLY on the page in the same fashion over and over again, so when it comes to the test I have my little steps laid out everywhere.
If it's more of a matter of not knowing algebraic stuff, I'd just work integrals over and over until you recognize the "tricks" (tangent, etc.) and brush up on things of that nature.
For me, it also helps to try and "teach" someone the problem, preferably someone who also knows the material. Verbalizing steps and whatnot really helps it sink into your brain as you try to teach it.
Don't feel bad, Calc II is defenitely the hardest of the three. I'm in Calc III this semster and it's one of the easiest classes I've ever taken, problem just because I worked so hard in calc II
Notes have never really helped me in a Math class. What I do is go through each chapter and more or less outline it, writing down equations and rules and whatever else I feel like I need to study. Then I go through and do the homeworks again, then finally end on practice exams.
Yah I'm the same way. I made a comment about the book earlier and the TC was like "psh naww brah them's problem examples are too easy \m/" (or something like that) but that wasn't my point. If you're only use of the book is to dig up example problems and not, say, all those words in between the problems, well, that's a problem!
But if you can drop it with a W(NOT a W-F, which says you failed AND couldn't finish)there's no shame. I actually did it in calc 3(yes yes I know I said it was easier, it was a 3 test class and I bombed the first test so absolutely due to overconfident lack of preparation I just dumped it and took it in the summer for the easy A)
But be careful doing that. If you've got loans or scholarships, you might invalidate yourself by dropping below fulltime status or dropping more than a certain percentage of your classes
Unfortunately the Withdraw period passed a week before the exam. And, at the time, I thought I had the hang of everything so dropping it didn't seem like it would have been necessary.
After this post I'll try and post a problem that I did in my homework (that I got wrong) and see if you guys can pinpoint where I screwed up. So far, you guys have been all been fantastic, and I can't thank you enough.
Actually guys. I don't think it's possible for me to get a C in this class anymore. I just did the math.
Exam 1: 73
Exam 2: 38
Adding both of them up I got 111/200 points (which is about a 55). So in order to get 70 on all of the exams I have to have about 210 points out of 300. Which means, in theory, I have to get a 99/100. Considering all the crap I've done already.... I completely doubt my abilities to make it.
Actually guys. I don't think it's possible for me to get a C in this class anymore. I just did the math.
Exam 1: 73
Exam 2: 38
Adding both of them up I got 111/200 points (which is about a 55). So in order to get 70 on all of the exams I have to have about 210 points out of 300. Which means, in theory, I have to get a 99/100. Considering all the crap I've done already.... I completely doubt my abilities to make it.
Well, keep in mind there may be a curve. Many courses (especially science/math ones) end up curving the final grade based on class performance. I was in a Physics class where literally no one in the class got better than a 50/100 on any test, but there were still people with A's.
Unless your professor has explicitly stated the grading criterion, just try to do your best. Or if you are really concerned, try to do a Withdrawal as someone here mentioned.
But so I can learn something here's a few I got wrong:
Improper Integrals #1:
Okay, since I don't know how to type the integration symbol (S looking thing) I'll just type out the problem.
Integration from (-infinity to 0) of: 1/2x-5 dx
I started by changing the -infinity to t and setting the limit of t -> -infinity so it looked like:
Integration from t to 0 of: 1/2x-5 dx
Then I used substitution to integrate the above..... Hmm... I think I found out what i did wrong, but I'll tell you what I did (1/2x-5 was supposed to be a partial fraction, right?). u= 2x-5, du=2dx, dx=1/2du. So it ended up being:
Integration from t to 0 of: 1/u 1/2du
Now you take the 1/2 out of the integration and then integrate 1/u du which ended up looking like:
1/2(ln(u))
Now you plug u back in to the u above, and then plug in 0 and t into the equation.
1/2(ln(2(0)-5) - ln(2t-5))
Which ended up being:
1/2(ln(-5) - ln(2t-5))
and since ln(-5) doesn't exist I said it was divergent.
Since I think I found the issue, I'll post another one:
Integration from (-infinity to infinity) of: cos(PI)t dt
So I broke it into the following:
Integration from (-infinity to 0) of: cos(PI)t dt + Integration from (0 to infinity) of: cos(PI)t dt
Then proceeded to change the infinity symbols into t and T, and worked on one at a time. So:
Limit (T-> -infinity) Integration from (0 to T) of: cos(PI)t dt
Which ended up being:
Limit (T-> -infinity) -sin(PI)t from (0 to T)
Then I plugged in the symbols:
Limit (T-> -infinity) (-sin(PI)(0) + sin(PI)(T))
Which ended up being sin(PI)(T), which ended up being 0 on my paper.
Then I did the same thing for the other integral:
Integration from (0 to infinity) of: cos(PI)t dt
Limit (T-> infinity) Integration from (T to 0) of: cos(PI)t dt
Limit (T-> infinity) -sin(PI)t from (T to 0)
Limit (T-> -infinity) (-sin(PI)(T) + sin(PI)(0))
Actually guys. I don't think it's possible for me to get a C in this class anymore. I just did the math.
Exam 1: 73
Exam 2: 38
Adding both of them up I got 111/200 points (which is about a 55). So in order to get 70 on all of the exams I have to have about 210 points out of 300. Which means, in theory, I have to get a 99/100. Considering all the crap I've done already.... I completely doubt my abilities to make it.
Well, keep in mind there may be a curve. Many courses (especially science/math ones) end up curving the final grade based on class performance. I was in a Physics class where literally no one in the class got better than a 50/100 on any test, but there were still people with A's.
Unless your professor has explicitly stated the grading criterion, just try to do your best. Or if you are really concerned, try to do a Withdrawal as someone here mentioned.
Well his "curve" is set at this: The highest grade in the class is a 100. So my first exam was a 68, but it was out of 91 (highest grade) so it ended up being ~73. The second test was out of 100 (highest grade was 105) so there wasn't a curve on it.
I don't think he curves the final grade. I'm sure there is one smart person in there who is fucking me in my grade (though it's my fault for sucking so hard) and getting 100s on the homework problems.
But so I can learn something here's a few I got wrong:
Improper Integrals #1:
Okay, since I don't know how to type the integration symbol (S looking thing) I'll just type out the problem.
Integration from (-infinity to 0) of: 1/2x-5 dx
I started by changing the -infinity to t and setting the limit of t -> -infinity so it looked like:
Integration from t to 0 of: 1/2x-5 dx
Then I used substitution to integrate the above..... Hmm... I think I found out what i did wrong, but I'll tell you what I did (1/2x-5 was supposed to be a partial fraction, right?). u= 2x-5, du=2dx, dx=1/2du. So it ended up being:
Integration from t to 0 of: 1/u 1/2du
Now you take the 1/2 out of the integration and then integrate 1/u du which ended up looking like:
1/2(ln(u))
Now you plug u back in to the u above, and then plug in 0 and t into the equation.
1/2(ln(2(0)-5) - ln(2t-5))
Which ended up being:
1/2(ln(-5) - ln(2t-5))
and since ln(-5) doesn't exist I said it was divergent.
Since I think I found the issue, I'll post another one:
Integration from (-infinity to infinity) of: cos(PI)t dt
So I broke it into the following:
Integration from (-infinity to 0) of: cos(PI)t dt + Integration from (0 to infinity) of: cos(PI)t dt
Then proceeded to change the infinity symbols into t and T, and worked on one at a time. So:
Limit (T-> -infinity) Integration from (0 to T) of: cos(PI)t dt
Which ended up being:
Limit (T-> -infinity) -sin(PI)t from (0 to T)
Then I plugged in the symbols:
Limit (T-> -infinity) (-sin(PI)(0) + sin(PI)(T))
Which ended up being sin(PI)(T), which ended up being 0 on my paper.
Then I did the same thing for the other integral:
Integration from (0 to infinity) of: cos(PI)t dt
Limit (T-> infinity) Integration from (T to 0) of: cos(PI)t dt
Limit (T-> infinity) -sin(PI)t from (T to 0)
Limit (T-> -infinity) (-sin(PI)(T) + sin(PI)(0))
Ended up being 0 + 0. And Convergent.
So, on the first one, remember that the integral of 1/x isn't ln (x) it's ln(abs(x)) (abs = absolute value). So you should end up with limit (t-> -infinity) (1/2) * (ln(5)-ln(abs(2t-5)))
And then of course bad things happen anyway. And it diverges because you get ln(infinity) which...not so much.
On the second one... you know what the graph of the sine and cosine functions look like, right? Do either of those have a limit has you approach infinity/negative infinity? So neither of those limits exist so it diverges.
And this makes sense if you think about it: int from -pi/2 to pi/2 is 2, from -pi to pi is 0, -3pi/2 to 3pi/2 is -2, -2pi to 2pi is 0, etc forever. You'll never hit a hard value.
EDIT: Also, why that first integral is not partial fractions is that partial fractions requires two linear terms to start. You did the integration correctly. And I forgot the 1/2.
enlightenedbum on
Self-righteousness is incompatible with coalition building.
Ugh. I can't believe I didn't think about cos/sin being the "waves" on a graph at the time, it does make sense.
Thank you sir. I'm going to see if I can do a few more of these.
I shouldn't lead you too far astray because the same integral with sin x converges. Simple way to put it is that the sine is odd, and any odd function integrated from -a to a is 0. (Similarly an even function integrated from -a to a is 2 * the integral from 0 to a, which you could have used to possibly some advantage on that previous question to make it more clear)
Or you do the integral and get limit t-> infinity of -cos(t) +cos(-t). And cos(-t) = cos (t) so that is zero, despite neither of those limits existing.
Trig rules are fun!
Anyway, yeah keep doing problems and be careful, that absolute value thing is probably one of the most frequently forgotten things in calc, because a lot of the time it ends up working right even if you don't include it and people aren't anal enough to mark off because you forgot the || when grading.
enlightenedbum on
Self-righteousness is incompatible with coalition building.
Part of the reason why I was doing so poorly at first (which hurt me now, because I know that I could have received a much higher score on my first exam if I knew) was the fact that I was really, really intimidated by "e" and "ln". Going all the way up to Calc II, I didn't really know/work with ln or e, and everytime I saw it I got really nervous.
I eventually just went home and worked at them a lot, and I feel much more comfortable now.
Also: at me for forgetting the absolute value.
urahonky on
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Big DookieSmells great!Houston, TXRegistered Userregular
Part of the reason why I was doing so poorly at first (which hurt me now, because I know that I could have received a much higher score on my first exam if I knew) was the fact that I was really, really intimidated by "e" and "ln". Going all the way up to Calc II, I didn't really know/work with ln or e, and everytime I saw it I got really nervous.
I eventually just went home and worked at them a lot, and I feel much more comfortable now.
Also: at me for forgetting the absolute value.
Don't feel bad. When I looked at your first problem, I couldn't see an issue with it either because I also forget about the absolute value thing. Like bum said, it's a very common mistake. Did he count the whole problem as being wrong just for that, though? I can't imagine more than a point or two being taken off for something like that. Because otherwise it seems like you did it correctly.
Part of the reason why I was doing so poorly at first (which hurt me now, because I know that I could have received a much higher score on my first exam if I knew) was the fact that I was really, really intimidated by "e" and "ln". Going all the way up to Calc II, I didn't really know/work with ln or e, and everytime I saw it I got really nervous.
I eventually just went home and worked at them a lot, and I feel much more comfortable now.
Also: at me for forgetting the absolute value.
Don't feel bad. When I looked at your first problem, I couldn't see an issue with it either because I also forget about the absolute value thing. Like bum said, it's a very common mistake. Did he count the whole problem as being wrong just for that, though? I can't imagine more than a point or two being taken off for something like that. Because otherwise it seems like you did it correctly.
It took me a few minutes staring at that myself.
enlightenedbum on
Self-righteousness is incompatible with coalition building.
I did really well in Math up until Differential Equations (Calc 4 for all intensive purposes). The key is to keep doing problems until you 'get it'. It's kind of shitty advice but its true. Make sure you go to Labs and talk with the T.A.'s
Sometimes I wouldnt understand a problem until a TA explained it a little differently.
DE sucks balls though.
Greg USN on
FFXIV Petra Ironheart Infinity Mog 21 and over Free Company Sargatanas Server. Recruitment currently closed.
Part of the reason why I was doing so poorly at first (which hurt me now, because I know that I could have received a much higher score on my first exam if I knew) was the fact that I was really, really intimidated by "e" and "ln". Going all the way up to Calc II, I didn't really know/work with ln or e, and everytime I saw it I got really nervous.
I eventually just went home and worked at them a lot, and I feel much more comfortable now.
Also: at me for forgetting the absolute value.
Don't feel bad. When I looked at your first problem, I couldn't see an issue with it either because I also forget about the absolute value thing. Like bum said, it's a very common mistake. Did he count the whole problem as being wrong just for that, though? I can't imagine more than a point or two being taken off for something like that. Because otherwise it seems like you did it correctly.
Unfortunately he's the kinda guy that's: "Either it's 100% right, or it's 100% wrong." MAYBE partial credit for doing the RIGHT way (so my "ignoring" of absolute values was doing it the wrong way).
Part of the reason why I was doing so poorly at first (which hurt me now, because I know that I could have received a much higher score on my first exam if I knew) was the fact that I was really, really intimidated by "e" and "ln". Going all the way up to Calc II, I didn't really know/work with ln or e, and everytime I saw it I got really nervous.
I eventually just went home and worked at them a lot, and I feel much more comfortable now.
Also: at me for forgetting the absolute value.
Don't feel bad. When I looked at your first problem, I couldn't see an issue with it either because I also forget about the absolute value thing. Like bum said, it's a very common mistake. Did he count the whole problem as being wrong just for that, though? I can't imagine more than a point or two being taken off for something like that. Because otherwise it seems like you did it correctly.
Unfortunately he's the kinda guy that's: "Either it's 100% right, or it's 100% wrong." MAYBE partial credit for doing the RIGHT way (so my "ignoring" of absolute values was doing it the wrong way).
Have I mentioned your prof is an idiot? Though if he cares about memorization the process wouldn't matter much. Arggggh. In lots of ways the right answer is the least important bit.
enlightenedbum on
Self-righteousness is incompatible with coalition building.
Have I mentioned your prof is an idiot? Though if he cares about memorization the process wouldn't matter much. Arggggh. In lots of ways the right answer is the least important bit.
I wouldn't go quite so far as to say the correct answer is the least important part. I mean if your career involves math and you always get the wrong answer but your work was right, you're still going to be fired.
But at the same time I agree about the prof being an idiot. Partial credit really should be given for correct problem-solving. And math isn't about memorization, and him teaching it that way is doing no good for anyone in the class unfortunately.
Also, entirely unrelated and just a pet peeve of mine, Greg USN it's "for all intents and purposes" not "for all intensive purposes."
Daenris on
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Big DookieSmells great!Houston, TXRegistered Userregular
Part of the reason why I was doing so poorly at first (which hurt me now, because I know that I could have received a much higher score on my first exam if I knew) was the fact that I was really, really intimidated by "e" and "ln". Going all the way up to Calc II, I didn't really know/work with ln or e, and everytime I saw it I got really nervous.
I eventually just went home and worked at them a lot, and I feel much more comfortable now.
Also: at me for forgetting the absolute value.
Don't feel bad. When I looked at your first problem, I couldn't see an issue with it either because I also forget about the absolute value thing. Like bum said, it's a very common mistake. Did he count the whole problem as being wrong just for that, though? I can't imagine more than a point or two being taken off for something like that. Because otherwise it seems like you did it correctly.
Unfortunately he's the kinda guy that's: "Either it's 100% right, or it's 100% wrong." MAYBE partial credit for doing the RIGHT way (so my "ignoring" of absolute values was doing it the wrong way).
Oh. Well in that case, your problem is simple:
Your professor is a major douchebag.
Even if you have little chance of passing at this point, I would stick it out as others have said and just try to take in as much as you can. Then next semester, just retake the class with a more competent professor, if there is someone else teaching it. If not... at least you'll know what to expect and how to study for the class, since you've already taken it. I mean, still try to pass this semester, because you never know how he might have pity on you at the end. But if it doesn't turn out well, retaking one class isn't the end of the world.
Don't feel too bad. In my fluids class the class I got a 32/60 on the first test. Unfortunately, his grading scheme is 100% right or 95% wrong. For instance, I multiplied something by the wrong number (everything else was right) and I got docked full points.
Heh, yeah, my professor is indeed a douchebag. The ONLY redeeming feature is that he got rid of our lab sessions in favor of lecture. Math labs are completely and utterly useless and I wish every professor got rid of them.
But I'm not going to give up. I'll keep trying, even if it means I still fail. If I start to grasp SOME of the material, I'll just retake it next quarter. Hopefully I'll find out if I passed or failed by the time next quarter starts (WSU has a problem with posting final grades more than two-three weeks after the damn final.)
e: Yeah I heard fluids is a tough class too, sucks to have a bad professor AND a tough class.
Have I mentioned your prof is an idiot? Though if he cares about memorization the process wouldn't matter much. Arggggh. In lots of ways the right answer is the least important bit.
I wouldn't go quite so far as to say the correct answer is the least important part. I mean if your career involves math and you always get the wrong answer but your work was right, you're still going to be fired.
But at the same time I agree about the prof being an idiot. Partial credit really should be given for correct problem-solving. And math isn't about memorization, and him teaching it that way is doing no good for anyone in the class unfortunately.
Also, entirely unrelated and just a pet peeve of mine, Greg USN it's "for all intents and purposes" not "for all intensive purposes."
Remember, math major theory type here, which is where that perspective comes from. While in classes the correct answer is less important than the process. However, if you're, say, an engineer? Get it right!
enlightenedbum on
Self-righteousness is incompatible with coalition building.
I dunno, I all but failed calc 1 in high school, made an A in calc 1 in college, made a (painfully hard fought)B in calc 2, after the false start I mentioned earlier I made an easy A in calc 3, then an easy A in ODEs, then an easy A in PDEs, and somewhere in there an easy A in LA
So I'd say just muscle through calc 2, it's all downhill for the most part
I'm a grad student in applied mathematics and I teach an undergraduate calculus-based probability and statistics class. A few things:
1) I want to echoe the sentiment that practicing problems over and over until you get it right is the very best to learn mathematics.
2) Your teacher sounds like a douche. However in regards to the docking points for silly errors part, I'd like to emphasize how important it is to approach your teacher (at least once) if there's any question about why a problem was graded harshly. I almost always try to give partial credit wherever I can to my students, but inevitably I'll look back and wonder why I took off so many points. Go to your teacher with an attitude of, I'm not sure why I got so many points taken off, what can I do to prevent this in the future (as opposed to, give me points douchebag you grade too tough) and I'm sure he'll be understanding, and may even give you back points. You pay enough to go to college, I think you have the right to talk to the prof about whats going on.
3) Don't get discouraged. Ever. Life is hard, so get used to it. I always tell my students that even if they see no obvious applications for the math they're learning, they're learning how to solve problems, and if math is difficult for them, they learn how to deal with adversity. Just a few things to keep in mind.
So yesterday he dropped a huge bomb in the class. He told us that his final grade reflects like this:
(EXAM1 + EXAM2 + HOMEWORK)/300
OR
Final Exam
Whichever is the highest grade he will take and use that. So I'm not dead in the water just yet! Looks like I'm going to use everyone's study tips all weekend. I HAVE to get a C or better. I don't want to retake this class!!
Going back to the original post, just to clarify...you studied 8-9 hours in the two days preceding the test...how much did you study before that?
Take that Monday for example, unless by study you mean diligently practiced problems of all the same type, you probably retained about the last two hours worth of studying and wasted the preceding three or four
You need to be studying EVERY day you feasibly can, an hour or two, not cramming before the test. If you aren't learning the things as they come up in class, you're not developing the necessary knowledge to learn the next things, and are just wasting your time even going to class, and then forcing yourself to not just study but to actually teach yourself material that's been taught over the course of weeks and months in just a couple of days.
Yeah I know. The issue that I seem to have is that if I study too far out from an exam or whatever, I seem to have a terrible time retaining it. It's like my brain remembers only a few days worth of "studying" and then just shuts it out.
Since I have my final on Monday at 3pm, do you think it'd be wise for me to study on Saturday from 7 or 8pm till about midnight, then get some sleep, then study from when I get up until late that night?
Then before the test I print off some practice problems to see if I retained any of it?
So yesterday he dropped a huge bomb in the class. He told us that his final grade reflects like this:
(EXAM1 + EXAM2 + HOMEWORK)/300
OR
Final Exam
Whichever is the highest grade he will take and use that. So I'm not dead in the water just yet! Looks like I'm going to use everyone's study tips all weekend. I HAVE to get a C or better. I don't want to retake this class!!
What's your homework grade? I thought I recalled you saying in the thread that you do well on the homework, but I could be making that up.
So yesterday he dropped a huge bomb in the class. He told us that his final grade reflects like this:
(EXAM1 + EXAM2 + HOMEWORK)/300
OR
Final Exam
Whichever is the highest grade he will take and use that. So I'm not dead in the water just yet! Looks like I'm going to use everyone's study tips all weekend. I HAVE to get a C or better. I don't want to retake this class!!
What's your homework grade? I thought I recalled you saying in the thread that you do well on the homework, but I could be making that up.
Well, my lowest was a 12/20, but everything else has been 16/20 or higher.
Posts
Limed. But you need to understand that mathematics textbooks are SO different from regular textbooks. The information density ends up being pretty high in a lot of cases, so it's slow going. And it's a much more thoughtful process--you need to 'get it' instead of just blasting through. This can help a lot, though--you're sitting down and putting in a lot of conceptual thought, which lays a foundation for doing problems AND of course still helps you understand the concepts.
Ahh okay.
Bah, sorry for the late reply. Yeah Improper Integration is the ones that have them at infinity. Also, you have to find the ones that are either convergent/divergent at whatever number.
The ones with infinity seem easy, just sub the infinite symbol for "t" and then solve down for t. But I can't ever picture the convergent/divergent ones.
I'll post an example either today or tomorrow (crazy busy today for some reason).
This is wrong. Your professor is an idiot. Math is all about understanding a concept and then building on that concept to reach some more interesting conclusion.
As to your specific problem and how to study for math, obviously doing problems is the best method. But the setting you want to do problems depends on the person. For some people study groups are really good, you get to bounce ideas off each other and see what actually works. Others need to be alone. Personally I combined the group work up through AP Calc in high school and then for college courses, when I was really struggling, I just ignored it for a while and my subconscious frequently figured it out. I don't recommend that method obviously, just telling you what I did.
A lot of times, a tutor can be really helpful. I tutored for the math department at the University of Michigan while I was an undergrad for four years. And if you find the right one, they can do a really good job (or at least, I'd assume that's why people kept coming back to me :P).
Now you mentioned you were struggling with partial fractions, for example. They're tricky at first but if you think about it in terms of something simpler that you know how to do, it's not too difficult.
Here's a (simple) example:
You want to integrate something like 1/(x-3)(x+4) (generally speaking, a polynomial in the denominator which can be factored into linear terms).
Now obviously we don't have a rule for that, and something like u substitution doesn't work.
So what do we do?
Let's consider a simple concept from waaaay back in your math career. Least common denominators!
Obviously you know how to do something 1/2 + 1/3 = 5/6. 1/2= 3/6 and 1/3= 2/6 and then add, woo.
So logically 1/(x-3)(x+4) should be equal to something/(x-3) + something else/(x+4), right? And if we have those, those are easily integrated! So set up the equation:
1/(x-3)(x+4)=A/(x-3) + B/(x+4)
Next step is that fractions are evil and should be destroyed at all costs to we multiply both sides by (x-3)(x+4) and get:
1=A(x+4)+B(x-3)
Now we have two unknowns we want to solve for (A and
A=1/7 and B=-1/7.
So then to finally answer the question:
int(1/(x-3)(x+4))
=int(1/(7(x-3)) - 1/(7(x+4)))
=(1/7)ln(abs(x-3))-(1/7)ln(abs(x+4)) + C
So that's partial fractions and why it works. The other case is that you have something like (x^2 + 4) in the denominator, which obviously can't be factored. If that's the case, instead of having the numerator above it being a constant, it's a linear polynomial. (Ax +
Like: 1/(x^2 + 4)(x-3) = (Ax +
So:
1) Nothing you can do but partial fractions
2) Factor the denominator
3) Separate the denominator into its factors with variables in the numerators, set this equal to the original integrand.
3) Destroy the fractions!
4) Pick values of x (arbitrary, though frequently particular values will make your life easier (0, 1, -1 are good if you have non-linear terms. If you have linear terms pick values of x that make the linear term 0 like I did above in picking 3 and -4)
5) Solve for the variables that were in your numerator
6) Rewrite your integrand
7) Integrate with methods you already know
8) Don't forget your + C!
Sorry for the length on this, but that's my lesson on partial fractions.
Personally, in my degree (EE) so far, I've used partial fraction expansion more than just about any of the other concepts from Calc II. I still have a year left, so that may change, but they've been incredibly useful when analyzing circuits in the s domain. Of course, the lesson is that you will actually use most of this stuff at some point. I would imagine that, for CS, Sequences and Series will become very useful for you later on.
Oculus: TheBigDookie | XBL: Dook | NNID: BigDookie
I would agree in general. I can't really speak to the usefulness of the math, since I majored in, um, math so screw application, theory's where it's at, man!
But yeah, a lot of times math doesn't make sense and then it just clicks once you've done some number of problems or something fires in your brain. Keep doing problems, ask a friend who's good to help out, etc.
My best advice if you're too far in the hole right now is to drop the class, study your ass off, get a tutor next semester and try again. The added pressure of having to perform above average in a class you're already not doing well in can lead to fucking it up regardless. Unless you're racing to get your degree or you're bound to a tight departmental schedule, retaking a class shouldn't be a big deal. You'll have the benefit of learning the material twice, and having already picked up the basics you'll be in a better position to understand the material as opposed to just learning the steps.
Fail less!
Haha. No but seriously I'm failing Calculus right now as well. It kinda sucks.
When I wake up tomorrow morning and that paragraph makes any sense at all, I'm going to be astonished.
I do this same process for pretty much every math intensive course I take.
And don't sweat Calc II too much, it is definitely the hardest one.
Just work the problems over and over until you recognize patterns etc. For me (I'm strange) it helps to set up problems PHYSICALLY on the page in the same fashion over and over again, so when it comes to the test I have my little steps laid out everywhere.
If it's more of a matter of not knowing algebraic stuff, I'd just work integrals over and over until you recognize the "tricks" (tangent, etc.) and brush up on things of that nature.
For me, it also helps to try and "teach" someone the problem, preferably someone who also knows the material. Verbalizing steps and whatnot really helps it sink into your brain as you try to teach it.
Don't feel bad, Calc II is defenitely the hardest of the three. I'm in Calc III this semster and it's one of the easiest classes I've ever taken, problem just because I worked so hard in calc II
Yah I'm the same way. I made a comment about the book earlier and the TC was like "psh naww brah them's problem examples are too easy \m/" (or something like that) but that wasn't my point. If you're only use of the book is to dig up example problems and not, say, all those words in between the problems, well, that's a problem!
But if you can drop it with a W(NOT a W-F, which says you failed AND couldn't finish)there's no shame. I actually did it in calc 3(yes yes I know I said it was easier, it was a 3 test class and I bombed the first test so absolutely due to overconfident lack of preparation I just dumped it and took it in the summer for the easy A)
But be careful doing that. If you've got loans or scholarships, you might invalidate yourself by dropping below fulltime status or dropping more than a certain percentage of your classes
After this post I'll try and post a problem that I did in my homework (that I got wrong) and see if you guys can pinpoint where I screwed up. So far, you guys have been all been fantastic, and I can't thank you enough.
Exam 1: 73
Exam 2: 38
Adding both of them up I got 111/200 points (which is about a 55). So in order to get 70 on all of the exams I have to have about 210 points out of 300. Which means, in theory, I have to get a 99/100. Considering all the crap I've done already.... I completely doubt my abilities to make it.
Well, keep in mind there may be a curve. Many courses (especially science/math ones) end up curving the final grade based on class performance. I was in a Physics class where literally no one in the class got better than a 50/100 on any test, but there were still people with A's.
Unless your professor has explicitly stated the grading criterion, just try to do your best. Or if you are really concerned, try to do a Withdrawal as someone here mentioned.
Improper Integrals #1:
Integration from (-infinity to 0) of: 1/2x-5 dx
I started by changing the -infinity to t and setting the limit of t -> -infinity so it looked like:
Integration from t to 0 of: 1/2x-5 dx
Then I used substitution to integrate the above..... Hmm... I think I found out what i did wrong, but I'll tell you what I did (1/2x-5 was supposed to be a partial fraction, right?). u= 2x-5, du=2dx, dx=1/2du. So it ended up being:
Integration from t to 0 of: 1/u 1/2du
Now you take the 1/2 out of the integration and then integrate 1/u du which ended up looking like:
1/2(ln(u))
Now you plug u back in to the u above, and then plug in 0 and t into the equation.
1/2(ln(2(0)-5) - ln(2t-5))
Which ended up being:
1/2(ln(-5) - ln(2t-5))
and since ln(-5) doesn't exist I said it was divergent.
Since I think I found the issue, I'll post another one:
So I broke it into the following:
Integration from (-infinity to 0) of: cos(PI)t dt + Integration from (0 to infinity) of: cos(PI)t dt
Then proceeded to change the infinity symbols into t and T, and worked on one at a time. So:
Limit (T-> -infinity) Integration from (0 to T) of: cos(PI)t dt
Which ended up being:
Limit (T-> -infinity) -sin(PI)t from (0 to T)
Then I plugged in the symbols:
Limit (T-> -infinity) (-sin(PI)(0) + sin(PI)(T))
Which ended up being sin(PI)(T), which ended up being 0 on my paper.
Then I did the same thing for the other integral:
Integration from (0 to infinity) of: cos(PI)t dt
Limit (T-> infinity) Integration from (T to 0) of: cos(PI)t dt
Limit (T-> infinity) -sin(PI)t from (T to 0)
Limit (T-> -infinity) (-sin(PI)(T) + sin(PI)(0))
Ended up being 0 + 0. And Convergent.
Well his "curve" is set at this: The highest grade in the class is a 100. So my first exam was a 68, but it was out of 91 (highest grade) so it ended up being ~73. The second test was out of 100 (highest grade was 105) so there wasn't a curve on it.
I don't think he curves the final grade. I'm sure there is one smart person in there who is fucking me in my grade (though it's my fault for sucking so hard) and getting 100s on the homework problems.
So, on the first one, remember that the integral of 1/x isn't ln (x) it's ln(abs(x)) (abs = absolute value). So you should end up with
limit (t-> -infinity) (1/2) * (ln(5)-ln(abs(2t-5)))
And then of course bad things happen anyway. And it diverges because you get ln(infinity) which...not so much.
On the second one... you know what the graph of the sine and cosine functions look like, right? Do either of those have a limit has you approach infinity/negative infinity? So neither of those limits exist so it diverges.
And this makes sense if you think about it: int from -pi/2 to pi/2 is 2, from -pi to pi is 0, -3pi/2 to 3pi/2 is -2, -2pi to 2pi is 0, etc forever. You'll never hit a hard value.
EDIT: Also, why that first integral is not partial fractions is that partial fractions requires two linear terms to start. You did the integration correctly. And I forgot the 1/2.
Thank you sir. I'm going to see if I can do a few more of these.
I shouldn't lead you too far astray because the same integral with sin x converges. Simple way to put it is that the sine is odd, and any odd function integrated from -a to a is 0. (Similarly an even function integrated from -a to a is 2 * the integral from 0 to a, which you could have used to possibly some advantage on that previous question to make it more clear)
Or you do the integral and get limit t-> infinity of -cos(t) +cos(-t). And cos(-t) = cos (t) so that is zero, despite neither of those limits existing.
Trig rules are fun!
Anyway, yeah keep doing problems and be careful, that absolute value thing is probably one of the most frequently forgotten things in calc, because a lot of the time it ends up working right even if you don't include it and people aren't anal enough to mark off because you forgot the || when grading.
I eventually just went home and worked at them a lot, and I feel much more comfortable now.
Also:
Oculus: TheBigDookie | XBL: Dook | NNID: BigDookie
It took me a few minutes staring at that myself.
Sometimes I wouldnt understand a problem until a TA explained it a little differently.
DE sucks balls though.
Infinity Mog 21 and over Free Company Sargatanas Server. Recruitment currently closed.
Unfortunately he's the kinda guy that's: "Either it's 100% right, or it's 100% wrong." MAYBE partial credit for doing the RIGHT way (so my "ignoring" of absolute values was doing it the wrong way).
Have I mentioned your prof is an idiot? Though if he cares about memorization the process wouldn't matter much. Arggggh. In lots of ways the right answer is the least important bit.
I wouldn't go quite so far as to say the correct answer is the least important part. I mean if your career involves math and you always get the wrong answer but your work was right, you're still going to be fired.
But at the same time I agree about the prof being an idiot. Partial credit really should be given for correct problem-solving. And math isn't about memorization, and him teaching it that way is doing no good for anyone in the class unfortunately.
Also, entirely unrelated and just a pet peeve of mine, Greg USN it's "for all intents and purposes" not "for all intensive purposes."
Your professor is a major douchebag.
Even if you have little chance of passing at this point, I would stick it out as others have said and just try to take in as much as you can. Then next semester, just retake the class with a more competent professor, if there is someone else teaching it. If not... at least you'll know what to expect and how to study for the class, since you've already taken it. I mean, still try to pass this semester, because you never know how he might have pity on you at the end. But if it doesn't turn out well, retaking one class isn't the end of the world.
Oculus: TheBigDookie | XBL: Dook | NNID: BigDookie
Yea, so never mind shitty profs.
But I'm not going to give up. I'll keep trying, even if it means I still fail. If I start to grasp SOME of the material, I'll just retake it next quarter. Hopefully I'll find out if I passed or failed by the time next quarter starts (WSU has a problem with posting final grades more than two-three weeks after the damn final.)
e: Yeah I heard fluids is a tough class too, sucks to have a bad professor AND a tough class.
Remember, math major theory type here, which is where that perspective comes from. While in classes the correct answer is less important than the process. However, if you're, say, an engineer? Get it right!
Wow, haven't seen that for a while
I dunno, I all but failed calc 1 in high school, made an A in calc 1 in college, made a (painfully hard fought)B in calc 2, after the false start I mentioned earlier I made an easy A in calc 3, then an easy A in ODEs, then an easy A in PDEs, and somewhere in there an easy A in LA
So I'd say just muscle through calc 2, it's all downhill for the most part
1) I want to echoe the sentiment that practicing problems over and over until you get it right is the very best to learn mathematics.
2) Your teacher sounds like a douche. However in regards to the docking points for silly errors part, I'd like to emphasize how important it is to approach your teacher (at least once) if there's any question about why a problem was graded harshly. I almost always try to give partial credit wherever I can to my students, but inevitably I'll look back and wonder why I took off so many points. Go to your teacher with an attitude of, I'm not sure why I got so many points taken off, what can I do to prevent this in the future (as opposed to, give me points douchebag you grade too tough) and I'm sure he'll be understanding, and may even give you back points. You pay enough to go to college, I think you have the right to talk to the prof about whats going on.
3) Don't get discouraged. Ever. Life is hard, so get used to it. I always tell my students that even if they see no obvious applications for the math they're learning, they're learning how to solve problems, and if math is difficult for them, they learn how to deal with adversity. Just a few things to keep in mind.
So yesterday he dropped a huge bomb in the class. He told us that his final grade reflects like this:
(EXAM1 + EXAM2 + HOMEWORK)/300
OR
Final Exam
Whichever is the highest grade he will take and use that. So I'm not dead in the water just yet! Looks like I'm going to use everyone's study tips all weekend. I HAVE to get a C or better. I don't want to retake this class!!
Take that Monday for example, unless by study you mean diligently practiced problems of all the same type, you probably retained about the last two hours worth of studying and wasted the preceding three or four
You need to be studying EVERY day you feasibly can, an hour or two, not cramming before the test. If you aren't learning the things as they come up in class, you're not developing the necessary knowledge to learn the next things, and are just wasting your time even going to class, and then forcing yourself to not just study but to actually teach yourself material that's been taught over the course of weeks and months in just a couple of days.
Since I have my final on Monday at 3pm, do you think it'd be wise for me to study on Saturday from 7 or 8pm till about midnight, then get some sleep, then study from when I get up until late that night?
Then before the test I print off some practice problems to see if I retained any of it?
What's your homework grade? I thought I recalled you saying in the thread that you do well on the homework, but I could be making that up.
Well, my lowest was a 12/20, but everything else has been 16/20 or higher.