REFERENCE

Math reference tables

Symbols, Greek letters, logarithms, multiplication and addition tables.

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Concept	Definition / formula	Explanation
Numbers	Real numbers include rational numbers and irrational numbers.	A rational number is a/b with integers a,b and b ≠ 0.
Exponents	aᵐ × aⁿ = aᵐ⁺ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 for a ≠ 0.	A negative exponent means a reciprocal.
Numeral systems	A positional base-b numeral has value Σ digitᵢ × bⁱ.	Bases 2, 8, 10 and 16 are common.
Percentage	p% = p/100	Multiply a total by p/100 to find its p-percent share.
Per mille	p‰ = p/1000	1% = 10‰.
Parts per million	ppm = fraction × 10⁶	1% = 10,000 ppm. Mass and volume ratios must be distinguished.
Zero	a + 0 = a; a × 0 = 0	Division by zero is undefined. 0! = 1 by the factorial convention.
Prime numbers	A prime is an integer greater than 1 with exactly two positive divisors.	2 is the only even prime.
Euler’s number	e ≈ 2.718281828459045	e is the base of the natural logarithm.
Fibonacci numbers	F₀ = 0, F₁ = 1, Fₙ = Fₙ₋₁ + Fₙ₋₂	0, 1, 1, 2, 3, 5, 8, 13, …
Algebra	An equation asserts equality between expressions.	Apply the same valid operation to both sides; keep domain restrictions.
Factorial	n! = 1 × 2 × … × n; 0! = 1	Counts permutations of n distinct objects.
Logarithm	log_b(x) = y ⇔ bʸ = x	For real logarithms, x > 0, b > 0 and b ≠ 1.
Logarithm rules	log_b(xy) = log_b x + log_b y; log_b(x/y) = log_b x − log_b y	Arguments must be positive. log_b x = ln x / ln b.
Natural logarithm	ln(x) = log_e(x)	ln(eˣ) = x for real x.
Quadratic equation	ax² + bx + c = 0; x = (−b ± √(b²−4ac))/(2a)	Requires a ≠ 0. A negative discriminant gives non-real roots.
Trigonometry	sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse	For right triangles. tan θ = sin θ / cos θ where cos θ ≠ 0.
Arccos	cos⁻¹ x ∈ [0,π]	Real domain: −1 ≤ x ≤ 1.
Arcsin	sin⁻¹ x ∈ [−π/2,π/2]	Real domain: −1 ≤ x ≤ 1.
Arctan	tan⁻¹ x ∈ (−π/2,π/2)	Real domain: all real x.
Basic probability	P(A) = favourable outcomes / total equally likely outcomes	0 ≤ P(A) ≤ 1. The equally likely condition matters.
Expectation	E[X] = Σ xᵢ pᵢ	The probabilities of a discrete distribution sum to 1.
Variance	Var(X) = E[(X−E[X])²]	Population variance divides by N; the usual unbiased sample estimator divides by n−1.
Standard deviation	σ = √Var(X)	Standard deviation has the same unit as the observations.
Probability distribution	A discrete PMF gives P(X=x); a continuous PDF integrates to 1.	A continuous density value is not itself the probability of one exact point.
Normal distribution	f(x) = exp[−(x−μ)²/(2σ²)] / (σ√(2π))	Requires σ > 0; standardize with z = (x−μ)/σ.
Calculus	Differentiation measures local rates; integration accumulates quantities.	The fundamental theorem connects derivatives and definite integrals.
Derivative	d(xⁿ)/dx = n xⁿ⁻¹	Derivative of a constant is zero; product and chain rules handle compositions.
Laplace transform	L{f}(s) = ∫₀∞ e⁻ˢᵗ f(t) dt	L{1}=1/s (Re s>0), L{eᵃᵗ}=1/(s−a) (Re s>Re a).
Convolution	Discrete: (x*h)[n] = Σ x[k]h[n−k]	Continuous: (f*g)(t) = ∫ f(τ)g(t−τ)dτ when it exists.

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Symbols, Greek letters, logarithms, multiplication and addition tables. Reference entries and numeric tables are generated locally, with no remote document or account required.

Unicode glyphs depend on installed fonts. Math and electrical entries are educational references, not installation ratings or professional design specifications.

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