Math

Jaypee M. David, ECE | Holy Angel university | email: [email protected] | website: www.enjayneer.com

Mathematics

y=b – horizontal asymptote

x=a – vertical asymptote

maximum/minimum – extrema or absolute max / absolute min

trichotomy – a>b, a<b, a=b

t=20 min Φ=48 lb

R=6371 km or 3595 mi

Analyzing, interpreting… - statistics

(x+y)+z = x+(y+z) – associative

x+y – closure

multiplicative identity = 1

additive identity (complex) = 0+0j

imaginary zero – conjugate

ordered pair – ordered pair

nominal scale – identification

ordinal scale – ranked

interval scale – calculated & interpreted

ratio – arithmetic operation

quantitative variable - numerical

qualitative or categorical variable – non numerical

discrete variable – countable

continuous variable – can assume within a given range

Inferential statistics – sample results

Descriptive statistics – tables & graphs

Histogram – rectangle representation

Freq polygon –

Freq distribution -

Relative freq distribution

Riemann sum – sum of area of rectangles

Points in a plane – fund theorem anal geom.

m x n = size

m & n = dimension

+ elements at inverse

Row = 4

Column = 0

Mathematician’s toolbox – mathematical induction

Recursion – preceding

, if not stated

θ = parallax

Archimedes spiral – r=aθ

Descartes – exponent

Georg Cantor – theory of sets from study of infinity

Euclid – similar triangles, proportional sides

Upper bound - ≥1

Lower bound - ≤1

Richter Scale:

→

For bacteria:

k=1.386 →

For C-14

Half-life: 5568 yrs


c=escape velocity

F=kx

Max=mean + k (SD)

Min=mean – k (SD)

→ Chebyshev’s Theorem

→ lemniscate

r=aθ → Archimedes’ spiral

Cardioid:

→ 3 leafed rose

→ 4 leafed rose

→ circle tangent to y-axis

→ circle tangent to x-axis

θ=a, in line thru the origin

r = a, center of circle at origin

Order – order of the highest derivative

Richter Scale:

Q

Histogram – rectangular

Re = 3959 mi

Parallax shift – moon shift with an angle with background

Descartes – credited for exponents

De Moivre’s theorem – imaginary number raised to natural number powers


Imaginary zeros theorem – conjugate

Function – set of ordered pairs

Domain – first set of ordered pairs

Range – second set of ordered pairs

Mode –highest frequency of values

Median – middle number

Fundamental theory of analytic geometry – one is to one correspondence

Algebraic vector – ordered pair (a,b)

Geometric vector – plane, segment with a ray

Bounded – enclosed in a circle

Unbounded – cannot be enclosed in a circle

Sample – selection of few elements

Representative sample – represents the whole set of data

Population – collection of all elements

Random sample – equal chances to be chosen to represent the set of data

Corner point – intersection of two boundaries

Factored completely – non prime

FOIL – first out in last; used to solve binomial factors

Augmented matrix – reduction of matrix

Differential – involves functions and its derivatives

General solution – set of all solutions of a D.E.

Math

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