Download - Lesson 1
Circle:
Circumference of circle = 2πR
Pi is also known as Archimedes’ constant
Radians:
2π = 360 degrees
1 = 57 degrees
Area, A = πR^2
Sphere:
Surface Area, S = 4 πR^2
Volume, V = 4/3 πR^3
Trigonometry:
c b
a
Sin(a,c) = b/c
Cos(a,c) = a/c
Tan(a,c) = b/a = sin(a,c)/cos(a,c)
Important approximations for very small (<1degrees) angles (in units of radians):
Sin(a,c) = a,c
Cos(a,c) = 1
Tan(a,c) = a,c
Exponential Function:
f(x) = a^x
a = 2 (1,2,4,8,…)
Exponential Decay:
f(x) = a^-x
a = 2 (1, ½, ¼, …)
Logarithmic Functions:
f(x) = log(a,x)
log(a,a^x) = x
Most important bases: a=10 (decadic logarithm), a=e 2.71828… (natural logarithm)
Periodic Functions:
Use Sin and Cos to express periodic functions
Sin(alpha) = sin(alpha+360) = sin(alpha+2π)
Cos(alpha) = cos(alpha+360) = cos(alpha+2π)
Sin^2(alpha) + cos^2(alpha) = 1
Sin Graph
Cos Graph
Coordinates and Vectors
y
Y2 2
Y1 1
X1 X2 X
Point 1: (x1,y1) (vertical bracket)
Point 2: (x2,y2)
(xd, yd) = (x2,y2) – (x1,y1)
Distance, d = SQUAREROOT(xd^2 + yd^2), = SQUAREROOT(x2-x1)^2 + (y2-y1)^2
Basic Statistics:
Assumption: set of N numbers, (x1,x2,x3….xn)
Mean = 1/n (x1+x2+x3…+xn) or 1/n SUM(from 1 to N)(xi)