Math Techniques

Table of contents

1 Pre-Calculus 2 Calculus Technique 3 Number Theory 4 Easy Analysis (not always serious)

Pre-Calculus

• Farmer Optimizes Fence (hard pre-cal but easy calc)
• Design a Tin Can (harder pre-cal but easy calc)

Calculus Technique

• Minimum Trig Identities for Calculus
• Famous Limit
• Related Rates Example
• Factor or solve ax⁴ + bx² + c = 0
• Lines in Parametric Form (http://softsurfer.com/Archive/algorithm_0104/algorithm_0104B.htm)
• From a Point to a Plane, distance, etc.
• Better Ways to Integrate Quotients of Polynomials (Partial Fractions) (http://www.efnet-math.org/math_tech/partial_fractions.pdf)
• Integrating Factors for Nonlinear First Order ODEs -- New from Phantal (http://www.efnet-math.org/math_tech/integrating%20factors.pdf)

Number Theory

• Greatest common divisor, Least common multiple, Modular inverses, Extended Euclidean Algorithm, The Euclid Code
• Example Hyperbolic Quadratic Form (http://efnet-math.org/math_tech/HyperQuadForm.html) Solution
• Diophantine Equation (http://efnet-math.org/math_tech/dioph2.htm): 2^a + 3^b = 5^c Not elementary

Easy Analysis (not always serious)

• Tough Trig Series (http://www.efnet-math.org/math_tech/ToughTrig.html): and Really Tough Trig Series (http://www.efnet-math.org/math_tech/series5.pdf)
• Euler's Identity Expansion (http://www.efnet-math.org/Meta/e_x_times_cos_x.html) of e^xcos(x)
• Finding the Sine of 1 Degree (http://www.efnet-math.org/Meta/sine1.htm)
• L'Hôpital Rulez
• Nested Radicals from Ramanujan (http://www.efnet-math.org/math_tech/RamanujanRadicals.pdf)