A question on MATH progression.
I've never had a formal treatment on algebra topics, should I get my feet wet on those before starting Spivaks? Or can I get to that when I am done?
IF I indeed need to understand everything related to Algebra, should I give Artin a try?
i'm assuming you mean spivak's calculus
i've never read it but i don't think you need any abstract algebra for any calc 1-2 material
Apparently Spivaks Calculus is more like a intro to analysis book, so people say.
Do I need Algebra for that, what do you think?
probably not
but it's worth learning algebra anyway
the broc powder is full with calcium, too
Recall that the differential of f(x,y) is
df = (df/dx)dx + (df/dy)dy
Now look at the ODE you were given. It matches this form. This means that there could be a function f whose differential is the given ODE and whose value df = 0.
If this is true, then P = df/dx, Q = df/dy.
We know that the mixed partial derivatives of a function equal eachother, so an easy way to check if f exists is to take the derivative of P wrt y and the derivative of Q wrt x and see if they equal eachother.
In your case, they both equal -sin(y)cos(x) and so we know f exists. We call this ODE exact.
Now the task is to find f. You use the clues available to you.
Take the integral of P wrt x:
f(x,y) = -cos(x)cos(y) + C
We know C cannot be a function of x, since it disappears upon differentiation wrt x, so this becomes
f(x,y) = -cos(x)cos(y) + h(y)
Now take df/dy and see how it compares with Q.
df/dy = -cos(x)sin(y) + h'(y) = cos(x)sin(y)
h'(y) = 2cos(x)sin(y)
Integrate
h(y) = -2cos(x)cos(y) + C
Now we know what f is.
f(x,y) = -cos(x)cos(y) - 2cos(x)cos(y) + C
= -3cos(x)cos(y) + C
Since the differential of f is 0, we can say that f = D, some constant, since the differential of a constant is always 0.
D = -3cos(x)cos(y) + C
Combining constants and solving for y gives
y = arccos(C/cos(x))
Note: The constant of integration in h is usually ignored, since it always combines later.
I have another question, friend, to you or anybody who has any idea.
I am studying elementary geometry and I also read some of the Geometry chapters in Langs Basic Math, or what he calls ''Transformations'' (Mapping, Isometries, Congruences, etc)
After I was done, I wanted to move to a book called ''Introduction to Geometry'' by Coxeter which is another book which deals with geometry through transformations or algebra.
I suppose a treatment of abstract algebra would be preferable than any other training in calc?
> Studying CS
> Actually using a good language
Im fucking envious
I also see u are german, would you mind telling me where u study?
Drink water instead.
Again, why do you want to get rid of calcium?
Can anyone help me out with pic related please?