Calculus & Analysis

Mandelbrot Set

A famous fractal generated from a simple equation in the complex plane.

Numerical Integration

Visualizing Riemann sums, Trapezoidal, and Simpson's rules to approximate definite integrals.

Logistic Map & Chaos

Exploring bifurcation and deterministic chaos.

Taylor Series

Approximating functions with polynomials.

Complex Number Visualization

Complex Number Visualization

Euler's Formula

Visualizing e^(iθ) on the complex plane and the world's most beautiful equation.

Fibonacci & Golden Ratio

Exploring the Fibonacci sequence and its connection to the golden ratio.

Fourier Transform

Decompose a complex wave into simple sine waves.

Implicit Differentiation

Implicit Differentiation

Julia Set

A complex fractal exploring the boundary of bounded orbits for a fixed parameter c.

Laplace Transform

Laplace Transform

Riemann Zeta Function

Visualizing the path of the Riemann Zeta Function in the complex plane.

Differential Equations

Visualizing slope fields and numerical solutions to first-order ordinary differential equations.

Limits & Continuity

Limits & Continuity

Parametric Curves

Parametric Curves.

Gradient & Contour Plots

Visualize the relationship between scalar fields and their gradient vector fields.

Arc Length & Surface Area

Visualize how integrals are used to calculate the length of curves and the surface area of solids of revolution.

Power Series Convergence

Visualize how the sequence of partial sums behaves inside and outside the radius of convergence.

Divergence Theorem

Visualize the relationship between the surface integral of a vector field over a closed surface and the volume integral of its divergence.

Gradient Field & Vector Calculus

Visualize gradient vector fields, equipotential lines, and vector calculus operations.

Green's Theorem

Visualize the relationship between a line integral around a simple closed curve and a double integral over the plane region it encloses.

Improper Integrals

Visualize the convergence and divergence of improper integrals with infinite intervals or infinite discontinuities.

Jacobian Transformation

Visualize how 2D coordinate transformations scale local areas using the Jacobian determinant.

L'Hôpital's Rule

Evaluate limits of indeterminate forms using derivatives of the numerator and denominator.

Line Integrals

Visualize the calculation of work done by a vector field along various parametric paths.

Mean Value Theorem

Visualizing how secant lines relate to tangent lines for continuous and differentiable functions.

Partial Derivatives & Tangent Planes

Visualize 3D surfaces, partial derivatives as slopes, and the resulting tangent planes.

Sequences & Series Convergence

Visualize the convergence of sequences and series, exploring conditions for a limit to exist.

Stokes' Theorem

Visualize the relationship between the surface integral of the curl of a vector field over a surface and the line integral of the field around its boundary.

Curl & Divergence Fields

Visualize curl and divergence fields in vector calculus, exploring fluid flow and vector field operations.

Double & Triple Integrals

Visualize multi-variable integration by partitioning domains into sub-regions.

Epsilon-Delta Limits

Visualize the formal definition of a limit using epsilon and delta bounds.

Fixed Point Iteration

Visualize fixed-point iteration and cobweb plots for finding roots of functions.

Multivariable Chain Rule

Visualize the multivariable chain rule showing how changes in independent variables propagate to the dependent variable.

Polar & Spherical Coordinates

Visualize and explore polar and spherical coordinate systems and their transformations to Cartesian coordinates.

Rolle's Theorem

Visualize finding points where the derivative is zero for a function with equal endpoints.

Surface Integrals

Visualize the computation of flux for vector fields across parametrized 3D surfaces.

Lagrange Multipliers

Visualize how the gradient of the objective function aligns with the gradient of the constraint function at extreme points.

Residue Theorem

Evaluate complex contour integrals by summing enclosed pole residues.

Uniform Convergence

Visualize the difference between pointwise and uniform convergence of function sequences.

Wronskian & Linear Independence

Determine linear independence of functions using the Wronskian determinant.