Showing 12 results
Maclaurin Series Visualizer
Increase the polynomial degree to observe how Taylor/Maclaurin series mathematically trace transcendental functions like sin(x) and e^x.
Implicit Differentiation
Implicit differentiation analyzer for non-functions (Circles, Ellipses, Foliums). Evaluates dy/dx dynamically, reacting to both x and y inputs to map vertical and horizontal tangents.
Related Rates Visualizer
Related rates visualization using implicit chain rule integration with respect to time (dt). Demonstrates the geometric parameter shift paradox of Constant dV/dt impacting spherical radii and conical fill heights dynamically.
Solid of Revolution Volume
Volumetric solids of revolution visualizer computing the Washer Method natively via integral bounds. Calculates both standard axis limits and offset axis shifts dynamically.
Slope Field Explorer
Slope field generator plotting directional isoclines. Includes an interactive differential Euler-trace mechanism resolving specific math solutions when a distinct Initial Condition point is dropped onto the coordinate grid.
Integration by Parts
Integration by parts geometric derivation visualizing the separation of total paramteric bounding box $uv$ into constituent sub-integrals $\int v du$ and $\int u dv$ via animated slicing logic.
Improper Integrals Explorer
Improper integrals interactive limit testing. Visually computes limit convergence against infinity comparing $1/x$, $1/x^2$, and $e^{-x}$ behavior with dynamic auto-zooming coordinate geometries.
Logistic Growth Differential Eq
Differential logistic population map visualizing the $dP/dt = kP(1 - P/K)$ growth carrying capacity asymptote model. Sweeps dynamic background slopefields evaluating inflection velocity shifts mathematically derived from Partial Fractions.
Parametric Motion Vectors
Parametric Cartesian vector tracking framework decoupling $x$ and $y$ positional derivatives. Casts independent $\langle dx/dt, dy/dt \rangle$ vectors against the path map to visualize orthogonal component logic and resulting chain rule geometry.
Polar Curves & Area
Polar geometry visualizer tracking rotational $r(\theta)$ traces. Highlights integral sector area sweeps $A = 1/2 \int r^2 d\theta$ and visualizes the geometric backward-rendering anomaly when traversing negative radii.
Series Convergence Tests
Convergence testing interactive engine visually exposing the logical divergence of p-series compared with Alternating boundaries (AST bounce) and absolute factorial crushes dictated by Ratio limit laws.
Taylor/Maclaurin Polynomials
Taylor/Maclaurin generator interactively layering $n$-degree $f^{(n)}/n!$ polynomial sweeps over transcendental seeds ($\sin(x), e^x, \ln(1+x)$). Demonstrates active radius of convergence limits dynamically via Center-$c$ shifting.