#math - Mon 26 Feb 2007 between 00:00 and 00:19

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Cosmo-sanis anyone here knowledgeable with Second Solutions by reduction of order?
TRWBWhttp://www.sosmath.com/diffeq/second/reduction/reduction.html
Cosmo-sanah, thank you
Phylo% Integrate[x/E^(X), x]
mbotPhylo: x^2/(2*E^X)
Phylodoes case matter for x?
excelblueyes
they even matter on paper
Phyloindeed it does
lol, true
is there a simpler way other than integration by parts to solve x/E^(x)?
JIMJONESBALLINSuppose that <o,o>_1 and <o,o>_2 are two inner product spaces on a vector space V. Prove that <o,o> = <o,o>_1 + <o,o>_2 is also an inner product on V.
TRWBWJIMJONESBALLIN: what's the def of an innner product space? just to get it all out in the open
JIMJONESBALLIN: um, inner product
JIMJONESBALLINIts a Vector space over a field endowed with an inner product.
TRWBWJIMJONESBALLIN: so are you talking an arbitrary field or R or C or what?
JIMJONESBALLINThe question doesnt say. But I think its over F^n
No, my apologies. Its over |R
TRWBWJIMJONESBALLIN: so is your problem that you don't understand the question?
JIMJONESBALLIN: k
seb-_% Solve[a x x + b x + c == 0, x]
mbotseb-_: {{x -> (-b - Sqrt[b^2 - 4*a*c])/(2*a)}, {x -> (-b + Sqrt[b^2 - 4*a*c])/(2*a)}}
TRWBWJIMJONESBALLIN: is your question how to solve this, or what is the definition of an inner product?
JIMJONESBALLINI'm tryna prove it.
TRWBWJIMJONESBALLIN: what are you trying to prove? i'm asking do you know the definition of an inner product?
Phylo... if x and X are different, what is E as opposed to e?
|Steve|So show that <-,->_1 + <-,->_2 satisfies the properties of an inner product.
JIMJONESBALLINOh sorry, I thought you asked for the definition of an inner product space.
Phyloand why doesn't e^f(x) work?
TRWBW|Steve|: i'm trying to get at that. is his problem how to show it, or that he doesn't know what the definitions involved are?
Phylowhere E^f(x) does
JIMJONESBALLINAn inner product on a vs V is just a function that assigns to every ordered pair of vectors x and y in V a scalar in F denoted <x,y>
|Steve|Phylo: That was already answered. e is a variable, E is the base of the natural logarithm.
TRWBWJIMJONESBALLIN: just?
JIMJONESBALLINNo, more to follow.
TRWBWk
dn4[1+2xCos(x)+sin^2(x)]/[x^2+2xCos(x)+Cos^2(x)] <-- when reducing this fraction's "2xCos(x)" Does it = [1+1+sin^2(x)]/[x^2+1+Cos^2(x)] ?
|Steve|It's also F-linear in the first argument, etc.
TRWBW|Steve|: i'm sure you know it. ;)
JIMJONESBALLINsuch that for all x,y and z in V and all c in F we have: a) <x + z, y> = <x,y> + <z,y>

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