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--- user:afassett:start:math [2011/05/18 19:55] – [section 5] afassett
+++ user: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==
+.)<m size> ln((gz)/w) </m> = <m size> (ln(g)+ln(z))-ln(w) </m>\\
+.)<m size> ln(sqrt{a-17}) </m> = <m size> 1/2ln(a-17) </m>\\
+.)<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>\\
+.)<m size> lim{x right:2^+}{ln(x-2)} </m> = -INFINITY\\
+Find the derivative of the function for problems 5-11.\\
+.)<m size> f(x)=ln(2x) doubleright f prime(x)=1/x </m> \\
+.)<m size> f(x)=8x^2ln(8x) doubleright f prime(x)=8x+16x*ln(8x) </m>\\
+.)<m size> y=ln(xsqrt{x^2-1}) doubleright y prime =1/x+x/(x^2-1) </m>\\
+.)<m size> f(x)=ln((6x)/(x+3)) doubleright f prime(x)=3/(x(x+3)) </m>\\
+.)<m size> y=ln(sqrt{(x+6)/(x-6)}) doubleright y prime=-6/(x^2-36) </m>\\
+.)<m size> y=ln(root{6}{(x-3)/(x+3)}) doubleright y prime=1/(x^2-9) </m>\\
+.)<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\\
+.)<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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