Calc 2 is punching me in the chest

[CrunchBerries]

I am taking calc 2 online, and am currently finishing the part on "Strategy for Integration", where all the u-sub/trigsub/partial fraction/by parts are combining into a problem set. They were already challenging on their own, but combining all these is very tricky haha! Definitely not high school math anymore.

Don't get me wrong, I like math and I am happy taking this course. I just want to vent and I figure some people here may relate. Sometimes I go through the material and I totally feel defeated. I do a problem, then I look at the answer in the solutions manual, and it feels like a gut punch when I get it wrong. And I mean not just "forgot to include the minus sign from somewhere" wrong, but "I bought a plane ticket to France and landed in Australia" wrong.

I know I will figure it out and maybe end up with a decent 'mark', but I have a LOT of work ahead of me.

 

[jedishrfu]

Try checking out the corresponding videos at

www.mathispower4u.com

where you can some insight from a different perspective on the problems.

They are short 10 min videos usually solving a specific problem.

With respect to the plane ticket, there was a story of some european researchers who booke a trip to Monterrey for a conference and wound up in Monterrey Mexico not Monterey California where the conference was.

Here's more:

http://www.huffingtonpost.com/map-h...-the-wrong-flight-all-the-time_b_8160184.html

 

[phyzguy]

Knowing which method to apply to an integration problem (substitution, partial fractions, integration by parts...) only comes with practice. After you have worked a lot of problems, you will get a feeling for which method to apply to a given case. But even then, it is often a trial and error process. You try one substitution...no that didn't help...what about this substitution?..well, that made it a little easier, now maybe I can use partial fractions... Anyway, my advice is practice, practice, practice.

 

[CrunchBerries]

Thanks guys, I'll have to review all this for my assignments/exam so I will be revisiting some of these tips.

 

[Dr. Courtney]

Just learn to get back up and back out of blind alleys.

 

[dkotschessaa]

Sounds simply stupid, but take the questions you get wrong and just do them over and over. It's a bit of a combination of rote memory, understanding conceptually, and practicing the techniques/concepts. There might even be a tiny amount of muscle memory involved in writing it down, or at least the act of writing helps you somehow.

Calc II is a legitimate bugaboo for math students university wide, it seems. I don't know why it is consistently taught the same (bad) way year after year at every university.

However, it also happens to contain the most BEAUTIFUL things you will learn in calculus (like Taylor series and such). It's just impossible to appreciate them when you are feeling stupid about trying to do integration by parts.

Sounds like you are sufficiently motivated though. Good luck.

-Dave K

 

[dkotschessaa]

Oh, and one more thing... Since you are doing all these combinations, write out your problems a bit like a narrative or proof. "Using u-substitution - using integration by parts." Try to tell a story with your problem solving. Should make it more interesting and clear in your own mind.

 

[CrunchBerries]

I cannot wait for Taylor series! I was working on geometric series on my pre-calc course and thought there was something awesome about series and induction. I figure these get expanded on during that chapter. I think it will be a great cherry on the cake to end my course with.

Basically all the chapters ahead look very interesting; Applications of Integration (arc length, engineering/physics etc..), Differential Equations (Exponential growth), and finally Series and Sequences.

I will try narrating and see what happens. Also my studying habits do involve repeating some difficult problems.

When I took calc 1, there were times where I also felt similarly, and I did quite well with an A+. But this course seems to have more material to it and is more involved. I do prefer Calc 2 to Calc1 so far, but I do appreciate and embrace the fact that it is a notch above in a few ways.

Thanks for the input

 

[dkotschessaa]

I cannot wait for Taylor series! I was working on geometric series on my pre-calc course and thought there was something awesome about series and induction. I figure these get expanded on during that chapter. I think it will be a great cherry on the cake to end my course with.

Basically all the chapters ahead look very interesting; Applications of Integration (arc length, engineering/physics etc..), Differential Equations (Exponential growth), and finally Series and Sequences.

I will try narrating and see what happens. Also my studying habits do involve repeating some difficult problems.

When I took calc 1, there were times where I also felt similarly, and I did quite well with an A+. But this course seems to have more material to it and is more involved. I do prefer Calc 2 to Calc1 so far, but I do appreciate and embrace the fact that it is a notch above in a few ways.

Thanks for the input

Some people do not believe students when they say it - but Calc II -wherever it is taught - is notoriously difficult, even more so in some ways than the next level. There are any number of reasons for this we could probably spend a whole thread on.

I do appreciate that you are looking forward to the material though. That helps a lot.

-Dave K

 

[Mark44]

A major part of the difficulty is that, unlike differentiation, integration is less procedural. With practice, you get a variety of techniques down, but none of them are guaranteed to work. Differentiation, OTOH, is more-or-less straightforward, in that if you apply the rules correctly, you end up with the derivative.

 

[symbolipoint]

Interesting last couple of comments. Integration is like the inverse of differentiation. Differentiation goes in a less complicated way, but figuring out how to go back the other way 'seems harder'. This is like learning Multiplication and then find that learning Division is more unclear, with more things to think about and plan for.

 

[dkotschessaa]

A major part of the difficulty is that, unlike differentiation, integration is less procedural. With practice, you get a variety of techniques down, but none of them are guaranteed to work. Differentiation, OTOH, is more-or-less straightforward, in that if you apply the rules correctly, you end up with the derivative.

Interesting last couple of comments. Integration is like the inverse of differentiation. Differentiation goes in a less complicated way, but figuring out how to go back the other way 'seems harder'. This is like learning Multiplication and then find that learning Division is more unclear, with more things to think about and plan for.

Very true. We could possibly pin this down somewhat formally by talking about the functions of differentiation and division on the set of real numbers...

 

[TJGilb]

Solving those really hard problems now will make your life so much easier in the future. Also, in case you haven't been taught it, look up the tabular method for integration by parts (they never touched it in Calc 2 for me). I find it makes it so much easier in a lot of cases.

 

[dkotschessaa]

Solving those really hard problems now will make your life so much easier in the future. Also, in case you haven't been taught it, look up the tabular method for integration by parts (they never touched it in Calc 2 for me). I find it makes it so much easier in a lot of cases.

That's pretty neat:

http://www.hyper-ad.com/tutoring/int_parts.htm

It will (it seems at least from the example) give the right answer, but I'm not sure how well it would go over on a test. I'd definitely ask the professor whether this was allowable before doing it there.

-Dave K

 

[CrunchBerries]

The advice in this thread has been very helpful! I have come a long way since then.

I have a mid-term next tuesday, and I am very confident on most of the material, but i would like to consolidate integration techniques. What would you recommend for me to do at this point? I have already lined up more practoce problems with available solutions.. but if there are any more ideas i would be glad to try something different.

Thanks guys, and this has been TOUGH but rewarding.