Date & Time
Converts any date between Gregorian, Julian and the fixed Hebrew calendar: molad of the month, the four dehiyyot postponement judgments, keviyah year type, the weekly Torah portion (parasha) for Israel or Diaspora, the Omer count, the full festival schedule of the Hebrew year and the Anno Mundi era in Hebrew letters.
hebrew-calendar-bilingual-date-converterFinance
Side-by-side monthly rent-vs-buy simulation: mortgage amortization, property tax, insurance, HOA and maintenance against rent plus renter insurance; the renter invests the down payment and monthly savings at an opportunity-cost rate. Outputs break-even year on net sale proceeds, per-year differential NPV, SALT-cap-aware after-tax cash flows, a differential IRR, and a ±20% tornado sensitivity chart.
rent-vs-buy-total-cost-of-ownership-mortgage-tax-insurance-maintenance-irr-tutorMath & Numbers
Enumerate primes up to 10⁷ (or within [m, n]) with the classic sieve; shows base primes, crossing-out operations, exact counts, and up to 200 primes.
sieve-of-eratosthenesMath & Numbers
Two-person zero-sum games: saddle-point test first, then mixed strategies from a single-phase simplex LP with dual shadow prices, verified by security-level checks.
game-theory-zero-sumMath & Numbers
Dijkstra with a full per-iteration trace: settled nodes, relaxations, distance table, and the final path; undirected or directed, negative weights rejected, unreachable targets reported.
graph-shortest-pathMath & Numbers
Numeric convergence tests for Σ aₙ: nth-term, ratio, root, p-series comparison, and integral test; alternating series classified by Leibniz with a sum estimate.
series-convergence-testerMath & Numbers
Union, intersection, difference, symmetric difference, and Cartesian product of two comma-separated sets, with cardinalities and capped pair display.
set-operations-calculatorMath & Numbers
Table lookup of the unilateral Z-transform for 11 standard pairs, with parameter substitution, region of convergence, derivation note, and optional numeric X(z₀) evaluation.
z-transform-calculatorMath & Numbers
Convert dilution notations 1:X ↔ 1/X ↔ percent, with dilution factor, parts, and mixing volumes.
dilution-ratio-converterMath & Numbers
Classical fourth-order Runge-Kutta for dy/dx = f(x, y): step table, k1–k4 stage details, final estimate, and optional exact-solution error column.
runge-kutta-rk4-solverMath & Numbers
Solve a·y'' + b·y' + c·y = f(x): characteristic roots, three homogeneous cases, undetermined coefficients with resonance, and C1/C2 from initial conditions.
second-order-ode-solverMath & Numbers
Compute remaining radionuclide activity A(t) = A₀·2^(−t/T½) with λ = ln2/T½ in Bq/Ci/dpm units, for Tc-99m, F-18 and other isotopes.
half-life-activity-decay