Showing 10 results
Vector Curvature & Acceleration
Vector-valued function analyzer showing velocity (tangent), acceleration vectors, curvature κ, and osculating circle with radius R=1/κ. Explore Parabola, Sine Wave, Spiral, and Astroid trajectories with animated particle motion.
Surface Area of Revolution
3D wireframe rendering of surfaces of revolution around the x-axis. Demonstrates S = ∫2πf(x)√(1+f'(x)²)dx with interactive rotation angle and bounds. Explore Sphere, Cone, Gabriel's Horn, and Sine Vase with drag-to-orbit camera.
Partial Fractions Decomposition
Step-by-step partial fractions decomposition walkthrough using the Heaviside Cover-Up Method. Color-coded algebraic steps for 4 integral types including factoring, coefficient solving, and natural log integration with u-substitution bypass detection.
Power Series: Interval of Convergence
Interactive power series convergence visualizer comparing partial sums S_N(x) against exact functions. Shows convergence interval with amber boundary lines, Ratio Test explanations, and endpoint analysis for e^x, geometric, ln, cos(x), and n^n x^n/n! series.
Polar Area Between Curves
Polar coordinate area calculator for enclosed regions between two curves. Computes ½∫(R²−r²)dθ via Simpson's rule with adjustable α and β bounds. Visualizes Circle vs Cardioid, Rose vs Circle, Limaçon vs Circle, and dual Rose comparisons.
Integration by Parts: Tabular Method
Step-by-step Tabular (Tic-Tac-Toe) Method for Integration by Parts with diagonal product visualization, alternating signs, and LIATE selection rule. Covers polynomial×exp, polynomial×trig, logarithmic, and cyclic eˣ·sin(x) cases.
SN1 vs SN2 Nucleophilic Substitution
Side-by-side SN1 vs SN2 comparison with kinetics, stereochemistry (racemization vs Walden inversion), step-by-step mechanism walkthroughs, and decision flowchart table. Covers substrate structure, nucleophile strength, solvent effects (protic vs aprotic), and LIATE selection.
Stereochemistry & Chirality
Four-section stereochemistry module covering chirality and enantiomers, R/S CIP priority assignment rules, diastereomers vs meso compounds, and optical activity with polarimetry. Includes pharmacology context (Thalidomide) and biological homochirality discussion.
Partial Derivatives 3D Visualizer
Interactive 3D wireframe surface visualizer for partial derivatives. Shows tangent lines in x-direction (∂f/∂x, red) and y-direction (∂f/∂y, green) with gradient magnitude. Drag-to-orbit camera. Explore Paraboloid, Saddle, Wavy, and Gaussian surfaces.
Double Integrals Volume Visualizer
3D double integral volume visualizer with depth-sorted translucent prism rendering. Adjustable Riemann sum subdivisions (n) demonstrate convergence to exact value. Compare approximation vs exact with error display. Explore Dome, Plane, Wavy, and Cone surfaces.