dubiumlabsMathematics

Mathematics

Mathematical analysis tools: explore functions, series, matrices, and more with integrated symbolic and numerical computation.

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Function AnalyzerMathematical analysisSolve equations and analyze single-variable functions: roots, derivative, integral, critical points and interactive plotTaylor SeriesMathematical analysisApproximate f(x) with the order-N Taylor polynomial, compute radius of convergence, Lagrange error bound, and visualize the approximation errorSequences and RecurrencesMathematical analysisExplore linear recurrences, modular Fibonacci, and the logistic map with stability, periodicity, and chaos visualizationsSymbolic Matrix AnalyzerAlgebraCompute characteristic polynomials, spectra, and exact diagonalization for matrices up to 4×4Complex Arithmetic & PhasorsAlgebraCalculate complex number operations (addition, subtraction, multiplication, division), convert between rectangular, polar and exponential forms, and compute nth roots via De Moivre's TheoremAnalytical TrigonometryTrigonometry and geometrySolve oblique triangles (SSS, SAS, ASA, AAS, SSA) and right triangles with the law of sines, cosines, derived metrics (area, inradius, circumradius, altitudes, medians) and interactive SVG visualizationUnit Circle & Trigonometric FunctionsTrigonometry and geometryExplore six trigonometric ratios on the unit circle, with exact values and reference angles; graph transformed trigonometric functions, their periods and asymptotes where they existLinear Regression (2D)Statistics and probabilityFit your (x, y) dataset by least squares with 4 linearisable models (linear, exponential, logarithmic, power). Reports R², RMSE and the LaTeX equation alongside a scatter + fitted curve plotProbability DistributionsStatistics and probabilityComputes probabilities, percentiles and moments for Normal, Binomial, Poisson, Exponential, Gamma, Beta, Student's t, Chi-square and F distributions. Features interactive density and cumulative plots, and critical-value lookupDescriptive StatisticsStatistics and probabilitySummarizes a column of data: mean, median, mode, standard deviation (sample and population), variance, CV, SEM, MAD, quartiles, IQR, skewness and kurtosis. Visualizes with a box-plot and histogram (Sturges/Freedman-Diaconis/Scott) and flags outliers via 1.5·IQRStatistical InferenceStatistics and probabilityHypothesis tests and confidence intervals: one- and two-sample t (Welch and pooled), paired t, z, proportions (1 and 2 samples), one-way ANOVA, χ² goodness of fit and independence (r×c table), variances (χ² and F) and p-value from a statistic. Returns the test statistic, degrees of freedom, p-value, critical value, CI, effect size and a decision vs α, with the rejection region chartedExtended Euclidean Algorithm: GCD, Bézout & CongruencesNumber theoryComputes GCD and LCM with the Euclidean division table, reconstructs the Bézout identity via back-substitution and solves linear Diophantine equations ax + by = c, congruences ax ≡ b (mod n) and modular inverses, with every solution class and exact verification over integers of up to 40 digitsChinese Remainder Theorem: Congruence SystemsNumber theoryCombines congruence systems with coprime or shared moduli, constructs the solution class with inverses and extended Euclid, and proves incompatibility using the GCD.Polynomial Long Division and Synthetic DivisionAlgebraDivides polynomials step by step with long division or synthetic division (Ruffini's rule), giving the exact quotient and remainder with fractions. Shows the full layout, checks P = D·Q + R and applies the remainder and factor theorems.