i got this problem in my midterm today and i’m eager to find out if i did it right… any math geeks around?
yakes, oh the horror multivarible calculus! breaks out into cold sweats as memorys of second year engineering comes flooding back.
I would help but that would be like doing your homework for you plus i haven’t touched a calculus book in years so I would be the wrong person for this.
i don’t see the “doing your homework” part… this is not homework…
i used to hate calculus myself, but the instructors here made me like it…
well I could be wrong but last time I did differiential equations which is what I assume you original equation is checking if a solution was right was trivial finding it not so. plonk you solution back into the orignal equation and see if it holds.
wow, that equation looks fun
Yeah, looks good. The way you did it is correct and the actual calculations seem to be fine, although I didn’t really look through them very thoroughly. Typical example for exact ODEs, all around the world (had to do very similar stuff when I took a lecture on ODEs).
Yep, that looks okay. The only “error” was in your description when solving for a and b. You said it’s “either or,” but it should be “both,” which is what you solve for, anyway, so its all good. :yes:
Could someone please point out how that applies in the real world.
I never did any calculus or algebra at school and here I sit.
The point I make is that the education system appears to fill your mind with a lot of meaningless stuff, yet appears to overlook the fact that the primary producer is the one that appears to do 98% of the work.
Still, I can appreciate the work you would need to do to learn all that stuff.
thanks everyone for the comments:)…
thanks Laurifer for pointing that out… what i love about this math instructor is he does everything logically and using English and he wants us to do the same. he made me believe math shouldn’t be like ancient scriptures that you had to struggle to understand.
azecraze… this particular topic is important because we used to learn math as if everything in life was deterministic and linear. in the real world, most things change in a non-uniform way so you need differential equations to express those…
this page has useful applications:
Basically all of science and technology have mathematics like this at their base. You can thank math for the computer and network that allows you to read this.
@azecraze ODE are pretty important in fluids, and countless other science and engineering subjects, the whole field of fluid simulations is based on the fact that some of these equations don’t have exact solutions and you must apply numerical methods to get one. no education system is ever perfect but some of the stuff you learn that might not be important to you can turn out to be critical to someone else doing their job.
Well, a big problem in the education of math. We’re discussing that a lot (although we’re not going to be teachers…it’s still in an interesting point). The main problem (at least in schools here) is that you often don’t see how things are connected to each other and why you actually need them. When I started to study maths, I certainly had not the slightest clue just how powerful math really is. The importance of all that and the “beauty” is utterly destroyed by the way it gets teached here…
That’s definitely a big problem in education. In my opinion, studying math purely for the beauty is reason enough, like those who study poetry or philosophy. However, I also use it daily for practical purposes, but that doesn’t diminish the beauty-factor in my mind.