Greek Letters
The ratio of a circle’s circumference to its diameter
π (pi)
sin(π/2)
1
d/dx (sin x)
cos x
3.14159
π
a² + b² = c²
Pythagorean Theorem
The big symbol used for summation
Σ (capital sigma)
cos(π)
-1
∫ 1/x dx
ln|x| + C
1.414
√2
A continuous function on a closed interval must reach a max and a min
Extreme Value Theorem
The usual symbol for standard deviation
σ (lowercase sigma)
sin(π/6)
1/2
The limit of sin(x)/x as x → 0
1
2.718
e
If a continuous function goes from negative to positive, it must hit zero somewhere in between
Intermediate Value Theorem
The usual letter for an angle on the unit circle
θ (theta)
cos(π/4)
√2/2
∫₀^∞ e^(−x²) dx
√π / 2
1.618, often found in art and nature
φ (the golden ratio)
Somewhere on the interval, the instantaneous rate of change equals the average rate of change
Mean Value Theorem
The two letters in the formal definition of a limit
ε and δ (epsilon and delta)
The (x, y) coordinates at 2π/3
(−1/2, √3/2)
The sum of 1/n² from n = 1 to ∞
π² / 6
e^(iπ) + 1 equals this
0
It says differentiation and integration are inverses
Fundamental Theorem of Calculus