Understanding Differentials and Integrals: A Practical Guide

[DeViLDuD3]

ok I want to clear my broad views upon calculus..
first of all I wuz taught calculus 2-3 years back with differentials and Integration.. and ever since iam not really interested in doing this because I want to know wot iam doing ? I want to know how do they occur naturally ? I mean like i know if there is a equation like 3x+4y I wud differentiate subtracting one from the variables and multiplying their power with coefficients.. now iam doing BE Telecommunication, 2nd year, 4 semester, In our semester we have a subject that's related to maths and we do differentiate and integrate in those subjects.. but iam still not able to get the perspective ?
like right now we are studying about cylindrical and spherical coordinates, I understood that in cylindrical coordinates fy is the ground distance covered by the point to the rectangular x-axis and p and z blah..
I want to get to the main point
that is..
I came across this formula..
thats the formula for surface element
and that is S=pdfy dz
I hope ur getting the formula ?
it was also depicted in the book with the help of a diagram ? but I didnt really get it..
there were these differential areas.. what are those?
we got through a problem in which we had to find volume and surface.. we used differntials and integrals using limits..
I just want to know what differentials and integrals are all about ?
I mean a practical example ? like what's differentials are integrals in nature? where do they exist? I want an example like if we write apple then yea an apple comes to our mind.. like what's the shape and color.. can I get such an example for differentials and Integrals ?
I really want to make myself clear on these two topics.. because I guess every application uses these two methods... and I never knew why do they always come in the middle.. and I hate it when I don't know anything abt it.. I just don't like adding and subtracting things like a dumb... and yea I may sound like a dumbster.. but can anyone please give me a huge lecture or explanation regarding differentials and integrals ? I would be really glad if so.. please help me !

 

[HallsofIvy]

ok I want to clear my broad views upon calculus..
first of all I wuz taught calculus 2-3 years back with differentials and Integration.. and ever since iam not really interested in doing this because I want to know wot iam doing ? I want to know how do they occur naturally ? I mean like i know if there is a equation like 3x+4y I wud differentiate subtracting one from the variables and multiplying their power with coefficients.. now iam doing BE Telecommunication, 2nd year, 4 semester, In our semester we have a subject that's related to maths and we do differentiate and integrate in those subjects.. but iam still not able to get the perspective ?
like right now we are studying about cylindrical and spherical coordinates, I understood that in cylindrical coordinates fy is the ground distance covered by the point to the rectangular x-axis and p and z blah..
I want to get to the main point
that is..
I came across this formula..
thats the formula for surface element
and that is S=pdfy dz
I hope ur getting the formula ?
it was also depicted in the book with the help of a diagram ? but I didnt really get it..
there were these differential areas.. what are those?
we got through a problem in which we had to find volume and surface.. we used differntials and integrals using limits..
I just want to know what differentials and integrals are all about ?
I mean a practical example ? like what's differentials are integrals in nature? where do they exist? I want an example like if we write apple then yea an apple comes to our mind.. like what's the shape and color.. can I get such an example for differentials and Integrals ?
I really want to make myself clear on these two topics.. because I guess every application uses these two methods... and I never knew why do they always come in the middle.. and I hate it when I don't know anything abt it.. I just don't like adding and subtracting things like a dumb... and yea I may sound like a dumbster.. but can anyone please give me a huge lecture or explanation regarding differentials and integrals ? I would be really glad if so.. please help me !

I would suggest you take a good course in Calculus since it appears you did not actually learn anything in the course you took "2-3 years back".

Oh, and a good English course would help also.

 

[DeViLDuD3]

:s ok dats rudE !

 

[Newtime]

No, "dats" not rude for HallsofIvy to point out that your post was nearly incomprehensible. Why should anyone bother giving you a "huge lecture regarding differentials and integrals" if you can't be bothered to make a coherent post? That said, the advice above is correct. If you really lack a fundamental understanding of the basic concepts of Calculus, it would be in your best interest to take the class again. If that isn't an option, a book like Morris Kline's "Calculus: An Intuitive and Physical Approach" might give you the specific type of understanding you're looking for.

 

[DeViLDuD3]

ahan well :)
Iam not totally dumb.. as you probably might'eve figured out from my posts.. but actually I want to learn more and more.. whatever we do.. whether they r derivations or laplace, we always come across integrals and differentials.. and I do solve them on my own.. but I don't really get the point ? seriously.. I just wonder why do they always come in the middle ? I probably have to read more yea that's right... but in this forum there are many people.. can even greatest minds.. would they help me out ? a teacher is always better than studying alone that's what I think..
that for the replies anyways :s

 

[symbolipoint]

DeViLDuD3 -
You did not learn Calculus, two to three years back. Your first question and discussion on this topic indicates this. You may have studied, but you did not learn. The best action is to study Calculus again, doing this yourself from a good college level Calculus book.
... Even if you did study Calculus a few years ago, having stayed away from it since then gives abundant opportunity to forget almost everything you knew.

 

[berkeman]

DeViLDuD3 and I have had a discussion via PM. I'd normally go back and clean up his posts to try to make them intelligible, but that's too much work at this point. He should hopefully come back and try to do a better job of posting now...