Numerical Tools for University Calculus

Documentation for package ‘vectorialcalculus’ version 2.0.0

Help Pages

-- V --

vc_accumulation	Evaluate a signed accumulation function
vc_arc_length	Approximate the length of a graph
vc_area	Compute geometric area between two graphs
vc_classify_critical	Classify a possible critical point of a real function
vc_classify_stationary	Assess a multivariable stationary candidate by the second derivative test
vc_concavity	Sample concavity and search for smooth inflection candidates
vc_critical_points	Search for critical-point candidates on a finite interval
vc_curl	Estimate the Cartesian curl of a spatial vector field
vc_curvature_torsion	Evaluate curvature and signed torsion of a spatial curve
vc_curve_length	Integrate speed along a spatial parametric curve
vc_curve_sample	Sample an oriented spatial parametric curve
vc_cylindrical_integrate	Integrate a Cartesian field over a cylindrical-coordinate solid
vc_cylindrical_surface	Sample a cylindrical surface generated by parallel straight rulings
vc_derivative	Approximate a derivative with finite differences
vc_differential	Compare a differential with a finite change
vc_directional	Approximate a directional derivative on its actual line restriction
vc_divergence	Estimate the divergence of a square vector field
vc_double_integrate	Integrate over a Cartesian region with nested fixed quadrature
vc_frenet_frame	Evaluate the Frenet frame of a spatial curve
vc_fundamental	Explore the fundamental theorem of calculus numerically
vc_gauss	Compare outward flux and volume divergence in Gauss' theorem
vc_gradient	Approximate the gradient of a scalar field
vc_green	Compare the two integrals in Green's circulation theorem
vc_hessian	Approximate a scalar-field Hessian with direct differences
vc_integral_compare	Compare numerical quadrature rules
vc_integrate	Approximate a signed definite integral
vc_jacobian	Approximate the Jacobian of a vector-valued function
vc_lagrange	Assess an equality-constrained candidate using Lagrange multipliers
vc_limit	Probe a finite numerical limit from one or both sides
vc_linearization	Construct a numerical total differential and affine local model
vc_line_integral	Integrate a scalar or vector field along a parametric curve
vc_newton	Newton-Raphson iteration with explicit termination diagnostics
vc_newton_system	Newton iteration for a square nonlinear system
vc_osculating_circle	Sample osculating circles of a spatial curve
vc_osculating_ribbon	Sample the osculating ribbon of a spatial curve
vc_partial	Approximate a coordinate partial derivative
vc_partition	Construct a regular or custom partition
vc_partition2d	Construct a rectangular product partition
vc_plot_accumulation	Explore accumulation and signed regions interactively
vc_plot_area	Display geometric area between sampled graphs
vc_plot_concavity	Plot sampled concavity and smooth inflection candidates
vc_plot_critical_points	Plot critical-point candidates and derivative evidence
vc_plot_curvature_torsion	Display stored curvature and torsion on a sampled spatial curve
vc_plot_curve	Display stored spatial curve samples
vc_plot_cylindrical_integral	Display stored sections of a cylindrical integration region
vc_plot_differential	Plot a differential and the actual finite change
vc_plot_directional	Plot a directional line restriction on a sampled scalar surface
vc_plot_double_integral	Display stored Cartesian integration sections
vc_plot_frenet_frame	Display a stored Frenet frame on a sampled spatial curve
vc_plot_gauss	Display the box and outward normals for a Gauss comparison
vc_plot_gradient	Plot a gradient with optional stored directional playback
vc_plot_green	Display the stored region and oriented boundary for a Green comparison
vc_plot_integral	Visualize signed numerical quadrature
vc_plot_lagrange	View equality constraints, objective contours and Lagrange gradients
vc_plot_limit	Plot finite limit probes without evaluating the approach point
vc_plot_linearization	Plot a candidate tangent plane, coordinate tangents and linearization error
vc_plot_line_integral	Display stored samples from a line integral
vc_plot_matrix	Inspect a numerical derivative matrix and its stored refinements
vc_plot_newton	Plot Newton iterations, tangents and numerical residuals
vc_plot_newton_system	Animate two-dimensional Newton system iterates and zero contours
vc_plot_osculating_circle	Display stored osculating circles
vc_plot_osculating_ribbon	Display a stored osculating ribbon
vc_plot_polar_integral	Display a stored polar integration domain in Cartesian coordinates
vc_plot_region	Display a stored planar region in 2D or as a horizontal plate
vc_plot_related_rates	Display the gradient and a stored related-rates velocity
vc_plot_revolution	Display a solid of revolution and optional section playback
vc_plot_riemann	Draw signed Riemann rectangles with optional refinement animation
vc_plot_riemann2d	Draw stored signed Riemann prisms independently of calculation
vc_plot_secant	Plot an interactive secant and its function
vc_plot_secant_convergence	Animate stored secants approaching a numerical tangent
vc_plot_solid_cartesian	Display stored Cartesian solid faces or wireframes
vc_plot_solid_cylindrical	Display stored cylindrical-solid patches or wireframes
vc_plot_solid_spherical	Display stored spherical shells and optional angular cuts
vc_plot_spherical_integral	Display stored radial fibers of a spherical integration region
vc_plot_stationary	Inspect two-dimensional stationary candidates and search evaluations
vc_plot_stationary_surface	Inspect stored stationary candidates on a sampled 3D graph
vc_plot_stokes	Display stored Stokes circulation and curl flux
vc_plot_surface	Display a stored surface patch
vc_plot_tangent	Plot an approximate tangent and its function
vc_plot_taylor	Compare a function and its numerical Taylor polynomial interactively
vc_plot_triple_integral	Display stored sections of a Cartesian triple-integration region
vc_plot_vector_field	Display stored field arrows and an optional trajectory
vc_polar_integrate	Integrate a Cartesian scalar field over a polar region
vc_region	Sample a planar region independently of integration
vc_related_rates	Assess and solve a missing rate on an implicit level constraint
vc_revolution	Compute a volume of revolution from a planar strip region
vc_riemann	Compute signed tagged Riemann sums
vc_riemann2d	Compute signed double Riemann sums and sampled cell statistics
vc_riemann2d_convergence	Tabulate double Riemann refinement
vc_riemann_convergence	Tabulate Riemann refinement without claiming a limit
vc_secant	Compute the secant through two points of a real function
vc_secant_convergence	Tabulate secants at decreasing steps
vc_solid_cartesian	Sample the six faces of a nested Cartesian solid
vc_solid_cylindrical	Sample a cylindrical solid using stored parameter-box faces
vc_solid_spherical	Sample spherical solids as stored parameter patches
vc_spherical_integrate	Integrate a Cartesian field over a spherical-coordinate region
vc_stationary_points	Search for multivariable stationary candidates from explicit starts
vc_stokes	Compare circulation and curl flux in Stokes' theorem
vc_streamline	Trace a spatial field trajectory with fixed-step RK4
vc_surface_area	Approximate the lateral area generated by revolving a graph
vc_surface_graph_integral	Integrate a scalar density or oriented flux on a graph
vc_surface_integral	Integrate area, scalar density or flux on a parameterized surface
vc_surface_sample	Sample a rectangular parameter patch in space
vc_tangent	Construct an approximate tangent line
vc_taylor	Numerical Taylor approximations of order one or two
vc_triple_integrate	Integrate over a nested Cartesian solid
vc_vector_field_sample	Sample a spatial vector field in a nested Cartesian solid