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Postby talitha cumi » Thu Nov 26, 2009 6:25 am

who are Mathematicians out there??.. can you give me some teachings on how to understand integral calculus in an easier way??.. or somehow, any websites?? ..thank you so much..

GODbless..
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Postby Dante » Thu Nov 26, 2009 12:13 pm

That's a rather vague question. There is no high road in mathematics for nobles, nor a low road for peasants, only one road which is hard work (Paraphrased from the depths of my memory). There is perhaps an elegant road and a clumsy one, but sometimes a clumsy solution provides more value then the elegant one, but often times the elegant one is more satisfying, if albeit more risky. However, do not worry, the hard work is good.

"The greater the difficulty, the more glory in surmounting it. Skillful pilots gain their reputation from storms and tempests."-Epicurus

As far as websites are concerned, Wolfram's Mathworld is an invaluable resource:
http://mathworld.wolfram.com/

Furthermore though... isn't it a tad bit late in the semester to finally be worrying about your ills in integral calculus?!

In the end:
"The secret of science is to ask the right questions, and it is the choice of the problem more than anything else that marks a man (or woman) of genius in the scientific world."-Sir Henry Tizard in C.P.Snow

And with that, all I can say is "What is an easy way to understand integral calculus?" I'm afraid is NOT the right question.
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Postby blkmage » Thu Nov 26, 2009 12:42 pm

The theory of integral calculus (like Riemann sums and antiderivatives and stuff) is pretty much in the proofs of all the theorems that lead up to it and I don't think there's any other way to explain it. If you're asking for an easier way to compute integrals, then the answer is that unfortunately, it's a lot of intuition you'll have to build up. Integrals are a fairly different beast from differentiation, in that generally, there's no simple algorithm for you to follow.

Of course, there are patterns to look out for and tricks that will make computations easier (none of which come to mind since I haven't done integration in a while, something I'm worried about when I have to take another analysis class soon), but in general, the only way to get better is to do TONS of integrals until you're comfortable with them.
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Postby Technomancer » Thu Nov 26, 2009 6:29 pm

talitha cumi (post: 1357973) wrote:who are Mathematicians out there??.. can you give me some teachings on how to understand integral calculus in an easier way??.. or somehow, any websites?? ..thank you so much..

GODbless..


The short answer is that it depends on what your actual difficulties are. Personally, I've found that the best book is Stewart, so you might want to try consulting that, or other books in your school's library if you feel your current text is lacking.

I'd also strongly recommend Schaum's Outlines, which will walk you through a variety of sample problems.
The scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.

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Postby talitha cumi » Thu Nov 26, 2009 10:24 pm

Thank you for your precise replies. I didn't expect such answers like these. It seems like I'm really dealing with Mathematicians in here [hehe].. Honestly, my simple brain can't totally understand everything that you wrote but it doesn't matter. I just need some encouragements! You made me realize that I don't have to be a "genius" to pass the said subject. All I need is to do my best and HARD WORK is the best (of course with GOD's guidance as well)..

By d way Pascal, it's just the beginning of second sem here in our university so it's not yet that late I guess. hehe..

Again, thank you so much guys! Godspeed!
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Postby Dante » Fri Nov 27, 2009 1:38 pm

... Engineer's must be good with math, it is the language of their art, they may not be as fluent in it as physicists (because you know, physicists are better at everything :P), but they still must understand it well enough so that it can be a useful tool in projects... and if 30-20% of your math is wrong, a project with say 100 intermediate problems can have less then 2E-8% probability of success...

Also about some of your English... e.g. "d" = "the". If I saw that too much on a lab report in my PHY 112 Lab, I'd at least threaten point loss for language deficiencies like that. Your in college now, a certain mastery of English should at least be attempted.

...I suppose I'm just being a mean old goat. Good luck.
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Postby talitha cumi » Fri Nov 27, 2009 8:44 pm

..haha.. it's okay.. I mean, I don't really do that in school reports or anything connected in my studies.. I just thought that I don't have to be formal in writing in here but still, thank you for the reminders.

..Actually, you're not mean.. You're just maybe a 100% frank human being (which is the opposite of me)..

..Sorry for the errors.. Don't worry, I'm not offended.
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[color="Lime"][SIZE="4"]LORD[/SIZE][/color], somewhere in the middle, You'll find me...

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Postby blkmage » Fri Nov 27, 2009 10:26 pm

Pascal (post: 1358134) wrote:... Engineer's must be good with math, it is the language of their art, they may not be as fluent in it as physicists (because you know, physicists are better at everything :P), but they still must understand it well enough so that it can be a useful tool in projects... and if 30-20% of your math is wrong, a project with say 100 intermediate problems can have less then 2E-8% probability of success...


From my experience with undergraduate engineering mathematics, my impression was that they're more concerned with the mechanical aspects of math and the applications rather than the art and rigour. And it's this that was a big part of my decision to switch majors.

I started out as a software engineering major, which is a combination of computer science (which is considered math at my school) with engineering, so our program had us take engineering calculus and linear algebra, but we also had to take classical algebra, which was basically basic number theory with divisibility and primes and stuff.

Essentially, I found that the engineering maths just steamrolled over everything beautiful and enjoyable about math that I still had in my actual math course. After two semesters of this, I decided that I liked doing math more than doing useful things with math, so I switched my major to computer science and pure math.

I wouldn't say it's been easier or smoother, but dang, Galois theory is way cooler than software requirements and specification.
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Postby Technomancer » Sat Nov 28, 2009 4:41 am

blkmage (post: 1358201) wrote:From my experience with undergraduate engineering mathematics, my impression was that they're more concerned with the mechanical aspects of math and the applications rather than the art and rigour. And it's this that was a big part of my decision to switch majors.


I would say there was a fair bit of rigour in my courses. While we certainly didn't go into the sort of minutae that mathematicians do, it was deemed essential that we understand the principles and the basic derivations rather than say simply being told that method X solves problem Y. It was important to not merely understand how to use a method but why (and at times, why not).

On the other hand, the 1st year linear algebra course that I TA'd, was definitely not the equal of the one that I'd taken myself. Worse, they've even dropped the Complex Analysis requirement.
The scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.

Neil Postman
(The End of Education)

Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge

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