The Math [[http://lab46.corning-cc.edu/user/afassett/start|home page]] {{: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.) ln((gz)/w) = (ln(g)+ln(z))-ln(w) \\ 2.) ln(sqrt{a-17}) = 1/2ln(a-17) \\ 3.) 1/3(5ln(x+2)+ln(x)-ln(x^2-3)) = ln(root{3}{(x(x+2)^5)/(x^2-3)}) \\ 4.) lim{x right:2^+}{ln(x-2)} = -INFINITY\\ Find the derivative of the function for problems 5-11.\\ 5.) f(x)=ln(2x) doubleright f prime(x)=1/x \\ 6.) f(x)=8x^2ln(8x) doubleright f prime(x)=8x+16x*ln(8x) \\ 7.) y=ln(xsqrt{x^2-1}) doubleright y prime =1/x+x/(x^2-1) \\ 8.) f(x)=ln((6x)/(x+3)) doubleright f prime(x)=3/(x(x+3)) \\ 9.) y=ln(sqrt{(x+6)/(x-6)}) doubleright y prime=-6/(x^2-36) \\ 10.) y=ln(root{6}{(x-3)/(x+3)}) doubleright y prime=1/(x^2-9) \\ 11.) f(x)=ln(x+sqrt{4+x^2}) doubleright f prime(x)=1/sqrt{4+x^2} \\ ==Examples part B== Consider the following\\ 1.) y=7x^2-ln(x), (1,7) \\ (a) Find an equation of the tangent line to the grap of //f// at the given point.\\ y=13x-6 \\ (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**\\ p_n(x)=f(0)+f'(0)x+f"(0)/2!+...+(f^n(0))/(n!)\\ Example 1.) ==Taylor polynomial== **Theorem**\\ p_n(x)=f(c)+f'(c)(x-c)+f"(c)(x-c)^2/2!+...f^n(c)(x-c)^n/n!\\ 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\\