Mathematics & Numerical Analysis Simulators

Visualize Fourier series expansions of square waves, triangular waves, and sawtooth waves. Animate the Gibbs phenomenon and convergence as the number of terms N increases.

Visualize Taylor series expansion of various functions up to nth order. Interactively confirm the range of approximation accuracy and the effect of expansion order.

Numerically solve ordinary differential equations using Euler, Heun (RK2), and Runge-Kutta (RK4) methods and compare accuracy. Includes visualization of local truncation error.

Compare and visualize linear, Lagrange, Newton, and cubic spline interpolation. Real-time confirmation of the relationship between number of data points and interpolation accuracy.

Calculate arithmetic operations, polar form conversion, and De Moivre's theorem for complex numbers. Visualize phasor diagrams and operations on the complex plane.

Calculate matrix addition/subtraction/multiplication, inverse, determinant, eigenvalues, and eigenvectors. Display LU decomposition and eigendecomposition steps.

Statistically estimate pi using the Monte Carlo method. Display real-time animation of convergence as the sample count increases.

Calculate hypothesis testing using z-test and t-test. Real-time visualization of significance level, p-value, and rejection region on normal/t-distribution graphs.

Real-time calculation of PDF, CDF, and percentile points for normal distributions with varying mean and standard deviation. Verify standardization and Z-transformation.

Calculate simple, multiple, and polynomial regression using the least squares method. Real-time display of regression line, coefficient of determination R², and residual analysis.

Calculate arithmetic rules for significant figures and propagation of rounding error and measurement uncertainty. Visualize IEEE 754 floating-point precision limits.

One-stop conversion of major engineering units including length, mass, pressure, temperature, energy, and angle. Supports SI, CGS, and Imperial systems.

Calculate complex integrals using Cauchy's integral theorem and the residue theorem. Interactive display of singularities, residues, and integration paths on the complex plane.

Generate expected value calculations, sensitivity analysis, and tornado diagrams from decision trees. Quantify decision-making under uncertainty using maximum expected value criteria.

Numerically solve first- and second-order ordinary differential equations using Euler, RK4, and Adams-Bashforth methods. Real-time comparison of solution accuracy and stability.

Calculate Economic Order Quantity (EOQ), reorder point, safety stock, and annual total cost using Wilson's formula. Visualize trade-off between inventory and ordering costs.

Calculate basic Laplace transform pairs and partial fraction decomposition. Real-time display of transfer function poles, zeros, step response, and impulse response.

Solve two- and three-variable linear programming problems using the simplex method. Graphically visualize feasible region, optimal solution, and sensitivity analysis.

Numerically compute definite integrals using trapezoidal rule, Simpson's rule, and Gauss quadrature. Compare convergence of interval count and error on a log-log graph.

Calculate minimum project duration, critical path, total float, and free float for activity networks using PERT/CPM. Gantt chart display included.

Calculate polarization state transformations using Jones vectors and Jones matrices. Poincaré sphere display of linear, circular, and elliptical polarization.

Calculate Z-transform definitions, inverse transforms, and partial fraction expansions. Visualize digital filter transfer functions, frequency responses, and impulse responses on the z-plane.