AsaTaiyo Posted January 13, 2005 Report Posted January 13, 2005 I was just randomly wondering if we could start up a calculus forum. I mean it probably would have to take a lot of support, but lets face it, calc is fun.
pgrmdave Posted January 13, 2005 Report Posted January 13, 2005 why wouldn't calc fit under the mathematics forum?
AsaTaiyo Posted January 13, 2005 Author Report Posted January 13, 2005 nevermind i guess it kinda fits in with mathmatics and physics.:) sorry
maddog Posted January 14, 2005 Report Posted January 14, 2005 I was just randomly wondering if we could start up a calculus forum. I mean it probably would have to take a lot of support, but lets face it, calc is fun. Start a Calculus thread and see who bytes... :) Maddog
Tim_Lou Posted January 14, 2005 Report Posted January 14, 2005 hmmm, what should we discuss then?integrals? if you guys really want a calculus group.... Tormod would probably agree. but a moderator will be needed.
Tim_Lou Posted January 14, 2005 Report Posted January 14, 2005 Anyway, i love calc, it rocks~! hmm, how about open up a statistics group... just a thought.
Bo Posted January 14, 2005 Report Posted January 14, 2005 calculus and statistics are all branches of mathematics, so i see no problem in starting a thread here! (please do if you've got something!) Bo
AsaTaiyo Posted January 14, 2005 Author Report Posted January 14, 2005 OK, in my calc class today we are doing trig substitution integrals . I was kinda wondering how the book gets these identities, because they show no proof and it really bothers me.cos^2(x) = (1/2)(1+cos(2x))sin^2(x) = (1/2)(1-cos(2x))As in cos(x)cos(x), or sin(x)sin(x) could someone help me in proving these identities
AsaTaiyo Posted January 14, 2005 Author Report Posted January 14, 2005 I know the reason Why We use the identities but It bothers me that I don't know where they originate from. Its for solving Integrals like; ∫ ((4-x^2)^(1/2))/xThe integral is from 1 to 2
Tim_Lou Posted January 14, 2005 Report Posted January 14, 2005 (cos x)^2 = ((cos x)^2)*2/2since 2(cos x)^2 -1 = cos 2x (from cos(x+y) = cosx cosy - sinx siny)therefore, it=(cos2x + 1)/2 (sin x)^2 = (sin x)^2 *2/2since 1-sinx^2 = cos 2xtherefore, it= -(cos 2x - 1)/2
maddog Posted January 15, 2005 Report Posted January 15, 2005 calculus and statistics are all branches of mathematics, so i see no problem in starting a thread here! (please do if you've got something!) Bo Myself, I am interested in Abstract Algebra, in particular Lie Groups. Kinda' specialized to bea whole group. I agree thread would be better. I'll think of what I want to post. Later. Maddog
Bo Posted January 15, 2005 Report Posted January 15, 2005 group theory is incredible interesting (i think).. So please tell us something! As for tim's proof, it is i think not complete, because you used another identity (cos(x+y)=stuff) All these identities are (more or less)easy to proof, using the exponential form of the cos and sin functions (see http://mathworld.wolfram.com/Sine.html , equation 2, for the sine version); I'm affraid i don't see a proof, without using this form... Bo
sanctus Posted January 16, 2005 Report Posted January 16, 2005 group theory is incredible interesting (i think).. So please tell us something! Now that after four months of trying to understand it I eventually progress and start to have some enlightements (just in time actually, the exam is in a month) and I agree it's very interesting. I'm doing now Dirac's theory with the Lorentz groups.... (that is what I should study instead of writing here... :hihi: ) I'm affraid i don't see a proof, without using this form... Bo I agree, it's the one that comes directly from the definition, but you could still try to proof it with the corresponding series..... :rant:
Bo Posted January 17, 2005 Report Posted January 17, 2005 best would of course be to prove it using elementary eculidean geometry on the unit circle... (which should be possible...) Bo
Turtle Posted January 18, 2005 Report Posted January 18, 2005 OK Turtle bites. I love the beauty of the calculus! I suck at the pencil work, but ohhhhh the functions! Infinite surfaces with finite volumns (or vers visa)! Simply beautiful! As to the trigonmetric identities; they are ultimately algebraic re=statements. Some see the pattern easily, others (like me) don't. Math is hard & that's why we do it! Now group theory; there's some meat. On my small page under Pictures are graphs that may be modeled under Group Theory: http://www.coasttocoastam.com/shows/2004/03/19.html Technically, my system is a Ring. wherin the elements of the group allow addition, subtraction, nultiplication, but NOT division. When division works on group elements as well, it is called a FIeld. :hihi:
maddog Posted January 19, 2005 Report Posted January 19, 2005 Now group theory; there's some meat. On my small page under Pictures are graphs that may be modeled under Group Theory: http://www.coasttocoastam.com/shows/2004/03/19.html Technically, my system is a Ring. wherin the elements of the group allow addition, subtraction, nultiplication, but NOT division. When division works on group elements as well, it is called a FIeld. :rant: I may have missed and will look again. Just to clarify -- Fields are Division Ring in whichthere is closure under division for the ring. I myself am interested in a subset of DivisionRings called Normed Algebras (not nessecarily Fields). :hihi: Maddog
Turtle Posted January 19, 2005 Report Posted January 19, 2005 Thanks for covering with some additional details dog. I tend to generalization & leave the details to the specialists. I get to see the forest that way. Again I pasted the wrong link; my page is at: http://home.comcast.net/~turtlediable/wsb/index.html :hihi:
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