Calculus Tools
Browse all available calculus tools.
Available tools
- Antiderivative Additive Constant Anchor Tool Compute antiderivative additive constant anchor from explicit bounded inputs.
- Calculus: Differential Area Local Scale Tool Return oriented and absolute local area multipliers from a supplied 2x2 differential Jacobian, not a global area transform.
- Calculus: Implicit Two Variable Local Slope Tool Compute the implicit tangent slope -Fx/Fy from already evaluated local partials, rejecting vertical/undefined slopes.
- Calculus: Leibniz Boundary Term Tool Compute only the signed upper/lower moving-boundary term in Leibniz differentiation from supplied endpoint value and speed.
- Calculus: Partial Elasticity At Supplied Point Tool Compute one dimensionless partial elasticity (x/f)*df/dx at an explicitly supplied point, rejecting zero function value; no model fitting.
- Calculus: Scalar Central Difference Error Term Tool Return the leading f-third*h^2/6 truncation term of a symmetric first-derivative difference under caller-established smoothness; not an error bound or derivative estimator.
- Calculus: Scalar Second Differential Contribution Tool Distinguish a scalar second differential from its one-half-weighted quadratic Taylor contribution using an explicit supplied local second derivative.
- Calculus: Stationary Point Second Derivative Sign Tool Apply the local second-derivative test only after the caller explicitly establishes stationarity; zero remains inconclusive.
- Calculus: Tangent Line From Point Derivative Tool Evaluate the point-derivative tangent-line linearization at one x; the derivative is caller established, not symbolically inferred.
- Calculus: Tangent Normal Slope Orthogonality Tool Check the finite-slope tangent/normal orthogonality relation m*n=-1 with explicit absolute residual tolerance; vertical/horizontal cases require vector representation.
- Chain Rule Three Stage Local Product Tool Calculate chain rule three stage local product from explicit caller-supplied inputs.
- Critical Point Second Derivative Discriminant Tool Calculate critical point second derivative discriminant from explicit caller-supplied inputs.
- Curvature Normalization Denominator Tool Return the planar graph-curvature denominator (1+slope²)^(3/2), using a hypot norm before cubing.
- Curve Arc Length Integrand Tool Calculate curve arc length integrand from explicit caller-supplied inputs.
- Definite Integral Calculator Approximate a finite real expression integral with 256-panel composite Simpson quadrature; the refinement error estimate assumes a smooth integrand and is not a certified bound or improper integral solver.
- Derivative Of Normalized Scalar Pair Tool Calculate derivative of normalized scalar pair from explicit caller-supplied inputs.
- Derivative Relative Condition Term Tool Calculate derivative relative condition term from explicit caller-supplied inputs.
- Derivative Under Affine Unit Change Tool Calculate derivative under affine unit change from explicit caller-supplied inputs.
- Derivative Unit Ratio Label Qualify an explicit derivative unit-ratio record by order text without simplifying units.
- Differential Form Wedge Sign Tool Calculate differential form wedge sign from explicit caller-supplied inputs.
- Endpoint Singularity Integrability Power Tool Test local integrability of x^power at zero on a positive finite interval.
- Endpoint Trapezoid Correction Term Compute the explicit endpoint trapezoid correction relative to a left rectangle on an oriented interval.
- Euler Homogeneity Local Residual Tool Calculate euler homogeneity local residual from explicit caller-supplied inputs.
- Finite Difference Node Spacing Ratio Tool Compute finite difference node spacing ratio from explicit bounded inputs.
- Gradient Level Set Tangent Orthogonality Tool Unnormalized supplied dot-product tolerance, with a separate regular-level flag.
- Graph Surface Area Integrand Tool Calculate graph surface area integrand from explicit caller-supplied inputs.
- Implicit Curve Vertical Tangent Flag Tool Exact first-derivative tests for a supplied planar implicit curve gradient.
- Implicit Levelset Gradient Normalizer Tool Compute implicit levelset gradient normalizer from explicit bounded inputs.
- Implicit Second Partial Diagonal Term Tool Calculate implicit second partial diagonal term from explicit caller-supplied inputs.
- Implicit Three Variable Partial Ratio Tool Compute implicit three variable partial ratio from explicit bounded inputs.
- Improper Tail Power Integrability Tool Test convergence of the positive power tail integral from one to infinity.
- Indefinite Integral Calculator Find a symbolic antiderivative for sums, monomials, constant factors and supported elementary functions of linear expressions, with a constant of integration.
- Integral Moving Bound Normal Sign Tool Compute integral moving bound normal sign from explicit bounded inputs.
- Integral Orientation Composition Sign Tool Compose explicitly supplied orientation signs without changing the integral magnitude.
- Integral Subinterval Orientation Tool Orient a supplied ascending-bound definite integral; coincident bounds return zero.
- Integration Substitution Endpoint Order Tool Compute integration substitution endpoint order from explicit bounded inputs.
- Inverse Function Local Derivative Tool Return the inverse function derivative at the corresponding image point from a supplied nonzero forward derivative. Local invertibility is assumed.
- Inverse Function Third Derivative Tool Calculate inverse function third derivative from explicit caller-supplied inputs.
- Linearization Relative Error Tool Compare a supplied local linear approximation with the actual nonzero function value using absolute relative error.
- Local Integral Rectangle Correction Compare an explicit oriented left-rectangle area with a supplied integral on the same units.
- Local Logarithmic Second Derivative Tool Compute local logarithmic second derivative from explicit bounded inputs.
- Local Relative Condition Number From Derivative Tool Compute local relative condition number from derivative from explicit bounded inputs.
- Log Domain Derivative Chain Factor Tool Compute log domain derivative chain factor from explicit bounded inputs.
- Logarithmic Coordinate Area Jacobian Tool Compute logarithmic coordinate area jacobian from explicit bounded inputs.
- Logarithmic Derivative Residue Term Tool Calculate logarithmic derivative residue term from explicit caller-supplied inputs.
- Logarithmic Time Derivative Factor Tool Calculate logarithmic time derivative factor from explicit caller-supplied inputs.
- Midpoint Rule Supplied Curvature Bound Tool Compute midpoint rule supplied curvature bound from explicit bounded inputs.
- Mixed Partial Commutator Residual Tool Calculate mixed partial commutator residual from explicit caller-supplied inputs.
- Multivariable Directional Derivative Contribution Tool Compute multivariable directional derivative contribution from explicit bounded inputs.
- Numerical Derivative Approximate first and second derivatives of a polynomial via central finite differences.
- One Sided Derivative Agreement Residual Subtract explicit left derivative from right derivative without asserting differentiability from approximate values.
- One Sided Slope Disagreement Tool Compare explicitly supplied one-sided slopes without estimating derivatives or proving differentiability.
- Parametric Curvature Numerator At Point Tool Calculate parametric curvature numerator at point from explicit caller-supplied inputs.
- Parametric Curve Local Turning Sign Tool Compute parametric curve local turning sign from explicit bounded inputs.
- Parametric Curve Osculating Radius Tool Calculate parametric curve osculating radius from explicit caller-supplied inputs.
- Parametric Speed Zero Domain Flag Tool Calculate parametric speed zero domain flag from explicit caller-supplied inputs.
- Product Rule Third Derivative Term Tool Calculate product rule third derivative term from explicit caller-supplied inputs.
- Scalar Composition Second Derivative Term Tool Compute scalar composition second derivative term from explicit bounded inputs.
- Scalar Critical Point Flatness Residual Tool Compute scalar critical point flatness residual from explicit bounded inputs.
- Scalar Derivative Error Propagation Factor Tool Compute scalar derivative error propagation factor from explicit bounded inputs.
- Scalar Schwarzian From Derivatives Tool Calculate scalar schwarzian from derivatives from explicit caller-supplied inputs.
- Scalar Second Order Taylor Remainder Bound Tool Compute scalar second order taylor remainder bound from explicit bounded inputs.
- Secant Derivative Discrepancy Tool Calculate secant derivative discrepancy from explicit caller-supplied inputs.
- Second Order Relative Elasticity Tool Calculate second order relative elasticity from explicit caller-supplied inputs.
- Simpson Integration Calculator Approximate a definite integral from evenly spaced samples over [xMin, xMax] using composite Simpson's rule (odd sample count required).
- Stationary Slope Curvature Ratio Tool Return the local Newton displacement for finding a stationary point from supplied first/second derivatives.
- Symbolic Derivative Differentiate real arithmetic and supported elementary functions with product, quotient, power and chain rules where differentiable; other symbols are held constant.
- Tangent Axis Intercept Tool Calculate tangent axis intercept from explicit caller-supplied inputs.
- Trapezoidal Integration Calculator Approximate a definite integral from evenly spaced samples over [xMin, xMax] using the composite trapezoidal rule.