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user:afassett:start:math [2011/05/18 14:58] – afassettuser:afassett:start:math [2011/06/02 18:15] (current) – [Number Systems] afassett
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 +<WRAP round box>
 +<WRAP centeralign muchbigger><WRAP muchbigger fgred><WRAP muchbigger>The Math</WRAP></WRAP>
 +[[http://lab46.corning-cc.edu/user/afassett/start|home page]]
 +</WRAP>
 +</WRAP>{{:user:afassett:start:beautyinmath.jpg|}}
 +
 +====Number Systems====
 +This is where basic C.S. can be applied, compared to the number system.\\
 +==Systems==
 +  * //N// - Natural  - 1, 2, 3, ...
 +  * //Z// - Integers - -3, -2, -1, 0 , 1, ...
 +  * //Q// - Rational - p/q where p and q are integers and q is not zero.   
 +
 +----
 +==Special number systems===
 +  * [[http://en.wikipedia.org/wiki/Algebraic_number|algebraic]] 
 +  * [[http://en.wikipedia.org/wiki/Complex_number|complex]]
 +  * [[http://en.wikipedia.org/wiki/P-adic_number|p-adic]]
 +  * [[http://en.wikipedia.org/wiki/Surreal_number|surreal]]
 +  * [[http://en.wikipedia.org/wiki/Hyperreal_number|hyperreal]]
 +===References===
 +http://en.wikipedia.org/wiki/Number_system\\
 +=====Calculus 2=====
 +====section 1====
 +
 +----
 +
 +====section 2====
 +
 +----
 +
 +====section 3====
 +
 +----
 +
 +====section 4====
 +
 +----
 +
 +====section 5====
 +===part 5.1===
 +==Examples part A==
 +1.)<m size> ln((gz)/w) </m> = <m size> (ln(g)+ln(z))-ln(w) </m>\\
 +2.)<m size> ln(sqrt{a-17}) </m> = <m size> 1/2ln(a-17) </m>\\
 +3.)<m size> 1/3(5ln(x+2)+ln(x)-ln(x^2-3)) </m> = <m size> ln(root{3}{(x(x+2)^5)/(x^2-3)}) </m>\\
 +4.)<m size> lim{x right:2^+}{ln(x-2)} </m> = -INFINITY\\
 +Find the derivative of the function for problems 5-11.\\
 +5.)<m size> f(x)=ln(2x) doubleright f prime(x)=1/x </m> \\
 +6.)<m size> f(x)=8x^2ln(8x) doubleright f prime(x)=8x+16x*ln(8x) </m>\\
 +7.)<m size> y=ln(xsqrt{x^2-1}) doubleright y prime =1/x+x/(x^2-1) </m>\\
 +8.)<m size> f(x)=ln((6x)/(x+3)) doubleright f prime(x)=3/(x(x+3)) </m>\\
 +9.)<m size> y=ln(sqrt{(x+6)/(x-6)}) doubleright y prime=-6/(x^2-36) </m>\\
 +10.)<m size> y=ln(root{6}{(x-3)/(x+3)}) doubleright y prime=1/(x^2-9) </m>\\
 +11.)<m size> f(x)=ln(x+sqrt{4+x^2}) doubleright f prime(x)=1/sqrt{4+x^2} </m>\\
 +==Examples part B==
 +Consider the following\\
 +1.)<m size> y=7x^2-ln(x), (1,7) </m>\\
 +(a) Find an equation of the tangent line to the grap of //f// at the given point.\\
 +<m size> y=13x-6 </m>\\
 +(b) Use a graphing utility to graph the function and its tangent line at the point.\\
 +===part 5.2===
 +===part 5.3===
 +===part 5.4===
 +===part 5.5===
 +===part 5.6===
 +===part 5.7===
 +===Test===
 +{{:user:afassett:start:plugin-exam1.pdf|}}
 +----
 +====section 6====
 +===part 6.1===
 +===part 6.2===
 +===Test===
 +{{:user:afassett:start:plugin-exam2.pdf|Exam 2}}
 +
 +----
 +
 +====section 7====
 +
 +====section 8====
 +===Test===
 +{{:user:afassett:start:plugin-exam3.pdf|}}
 +----
 +
 +====section 9====
 +===part 9.1===
 +===part 9.2===
 +===part 9.3===
 +===part 9.4===
 +===part 9.5===
 +===part 9.6===
 +===part 9.7===
 +==Maclaurin Polynomial==
 +**Theorem**\\
 +<m size>p_n(x)=f(0)+f'(0)x</m><m size>+f"(0)/2!</m><m size>+...+(f^n(0))/(n!)</m>\\
 +Example 1.)
 +
 +==Taylor polynomial==
 +**Theorem**\\
 +<m size>p_n(x)=f(c)+f'(c)(x-c)+f"(c)(x-c)^2/2!+...f^n(c)(x-c)^n/n!</m>\\
 +Example 1.)
 +===Test===
 +{{:user:afassett:start:plugin-exam4.pdf|}}
 +
 +----
 +
 +====section 10====
 +===Test===
 +{{:user:afassett:start:plugin-exam5.pdf|}}
 +===terminology & references===
 +http://en.wikipedia.org/wiki/Cycloid\\
 +http://www.thefreedictionary.com/prolate <- Math terms\\
 +http://en.wikipedia.org/wiki/Focus_%28geometry%29\\
 +http://en.wikipedia.org/wiki/Vertex_%28geometry%29\\
 +http://en.wikipedia.org/wiki/Hypocycloid\\
 +http://en.wikipedia.org/wiki/Witch_of_Agnesi\\
 +
 +----
 +
 +====section 11====
 +
 +----
 +
 +====section 12====
 +====Books & References====
 +[[http://www.amazon.com/Calculus-Single-Variable-Ron-Larson/dp/0547209983/ref=dp_ob_title_bk/184-6494487-0321267|Calculus of a Single Variable by some a major douche]]\\
 +[[http://www.dokuwiki.org/plugin:math2|Math syntax]] used on this page\\
 +[[http://wiki.erazor-zone.de/doku.php?id=wiki:projects:php:dokuwiki:plugins:gnuplot|gnuplot]]\\
 +[[http://www.amazon.com/Calculus-Review-Research-Education-Association/dp/0878911820/ref=sr_1_1?ie=UTF8&qid=1306716273&sr=8-1|Calculus Super Review]] by Research & Education Association\\
  

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