heres a cool trick i learnt regarding infinite decimal numbers -

ie

3.711711711711711711.....

let S = 3.711711711...

S= 3 + 711/1000 + 711/1000^2 + 711/1000^3....

see the pattern - the "ratio" is 1:1000 each time, each element in the series.

therefore 1000.S = 3711 + 711/1000 + 711/1000^2 + 711/1000^3....

1000.S - S = 3711- 3 (the infinite recurring decimals subtract and are removed from the picture)

999 S = 3708

S = 3708/999 or 412/111

pretty nifty !

## Wednesday, November 21, 2012

## Saturday, November 3, 2012

this had been a really tough semester ! the work isn't too hard - but there is so much of it.

The math has been really fun.

Project/Team Management not so much since my team are a bunch of lazy ass teenagers...sheesh...

Statistics...its ok.

Here's a breakdown of the Maths we've covered.

* Proof of Pythagoras

* Trig ratios

* Natural Numbers, integers, Rational Numbers

* Proof root(2) is not a fraction

* Real Numbers as infinite decimals

* Intervals, closed and open notation

* Domain and range of a function

* Inverse trig functions

* The unit circle

* Elementary trig properties

* Periodicity of sin cos and tan

* Graphing of Functions

* Slope of a line between two points

* Average velocity for positions given in terms of time

* Instantaneous velocity defined as a limit.

* Derivatives, elementary calculus

* Polar coordinates

* Addition formulae for angles, double and half angle formulae

* Addition of two wave functions

* Modulus

* The Product Rule for differentiation of two functions

* The Chain Rule for Differentiation

* Trig identities and Simplifications

* Polynomials / RemainderTheorem

* Factorisation of Polynomials

* Completion of the square

* Leibniz Notation

* Implicit differentiation

* Differentiation of sin(x) and thus other trig ratios including powers and multiple angles

* Complex numbers, modulus of and argument of.

* Properties of modulus and complex conjugate of a complex number

* De Moivere's Theorem

* Square and Cube roots of complex numbers

* Relation to factoring polynomial functions

* Simple harmonic Motion

* Defn of natural log as the area under the graph of 1/x for x> 0

* graphing Exponential functions

* Decay / Half life

* Decay / Half life

* Complex exponentials and their relation to trig functions

* Hyperbolic functions

* Derivatives of the inverse trig functions

* Local and Global maxima and minima, how to find them if they exist

* Vectors in R2 and R3 from both geometric POV and algebraic POV

* Length and dot product of vectors

* Length and dot product of vectors

* Angle between vectors, Orthogonality

* Parallel and perpendicular vectors

* Vector Cross Product

* Equations of lines and planes in R3

* Find a plane through 3 given non collinear points

* Row operations and simultaneous Equations

* Continuity on a point and on an interval.

* Max and min for continuous functions on closed bounding intervals

* Mean Value theorem, and consequence of a positive derivative

* Rolle's Theorem as a special case

* Verbally posed max min problems

* Snell's Law

* Intermediate Value Theorem

* Approximate Solutions by repeated bi-sections

* Distance between two parallel lines.

* Indefinite integration - example of falling body under constant gravity

* Differential eqn's for Projectiles

* Geometric Sequence and its limit

* Summation

* Parametric curves in the plane

* Slope and equation of the tangent line

* Power Series

* Gregory Series

* Maclaurin Series

* Binomial Series

* Escape Velocity under the inverse square law of attraction

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