Saturday, September 18, 2010

Step-by-step homework 3 problem 1

(please let me know if you like/dislike the way I am presenting this, if there is anything I should add or subtract, and most importantly -- if I am doing something completely incorrectly. I would like this to be a learning experience rather than simply sharing answers, yet I am afraid that this is more of the latter. Please post questions you have or different methods you may have used to find the answers. It's also worth noting that I am using OpenOffice Calc. It is 95% the same as Microsoft excel. One thing that I am noticing is that in the IF statement, it is requiring a semicolon (;) instead of a comma (,). There may be other differences as well)

First of all, I'd like to mention that an important tool that I use is WolframAlpha. It makes it easy to find any solution to a problem so that you at least have an idea what it is that you are aiming for. In the case of this problem I made the input:
e^x-3x^2=0
and received 3 answers
0.910008
-0.458962
3.373308
since we are dealing with the interval [0,1] we are obviously looking to achieve the value 0.910008.

now, when inputting into excel I have:







a0 b0 f(a0) f(b0) c0 f(c0)
0 1 =EXP(A2) - 3*(A2^2) =EXP(B2) - 3*(B2^2) =((D2*A2) - (C2*B2)) / (D2-C2) =EXP(E2)-3*(E2^2)


the value of c0 is the root of the secant line and is expressed by (s: wikipedia):


at this point we have to check signs
=IF(SIGN(C2)=SIGN(F2); E2; A2) for a0 and
=IF(SIGN(D2)=SIGN(F2); E2; B2) for b0

at this point, the cells can simply be extended and the answer should be filled out. By the 8th iteration the answer should match up.

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