Package: vectorialcalculus
Type: Package
Title: Numerical Tools for University Calculus
Version: 2.0.0
Authors@R: c(person("Julio", "Lizarazo Osorio", role = "aut"),
    person("Julian Mauricio", "Fajardo", email = "julian.fajardo1908@gmail.com",
    role = c("aut", "cre")))
Description: Independent reconstruction of numerical tools for teaching
    university calculus. Provides finite difference derivative approximations
    with numerical sensitivity diagnostics and local linear models. Optional
    interactive graphics illustrate secants, tangents, differentials and
    numerical Taylor polynomials of orders one and two. Includes finite limit
    probes, critical-point and concavity analysis, and Newton iteration with
    explicit numerical diagnostics. Provides signed Riemann sums, partition
    refinement, fixed and adaptive quadrature with error diagnostics, and
    optional interactive illustrations of numerical integration. Evaluates
    accumulation functions and compares their numerical derivatives with
    integrands while retaining quadrature and sensitivity diagnostics. Computes
    geometric areas, graph lengths, revolution volumes and surface areas,
    with separate interactive region and solid illustrations. Approximates
    coordinate partials, gradients and line-restriction directional derivatives
    without inferring total differentiability from finite coordinate probes.
    Provides candidate affine models and total differentials with actual-change
    comparisons and separate plane, section and tangent illustrations. Supports
    rectangular Jacobians, direct Hessian stencils and matrix refinement views
    with entry-level numerical sensitivity and roundoff diagnostics. Searches
    for multivariable stationary candidates with explicit starts, retained
    evaluation histories and conditional second derivative classifications.
    Solves square nonlinear systems with Newton iteration, Jacobian
    diagnostics, optional step damping and independent zero-contour playback.
    Assesses equality-constrained candidates using Lagrange multipliers,
    numerical rank and conditional tangent-space curvature diagnostics.
    Integrates Cartesian type I and II regions with nested fixed quadrature,
    retained inner diagnostics and independent sampled-domain graphics.
    Supports polar regions with a radial Jacobian and Cartesian domain views.
    Integrates nested Cartesian solids in six coordinate orders, retaining
    slice diagnostics with independent fiber and base-projection displays.
    Supports cylindrical-coordinate solids with a radial Jacobian and
    separate Cartesian fiber and polar-base views. Spherical regions use
    explicit azimuth, polar angle and radius with their volume Jacobian
    and an independent Cartesian radial-fiber display. Assesses implicit
    related rates with feasibility, differentiability hypotheses, denominator
    sensitivity diagnostics and a separate local velocity display. Provides
    product partitions, signed double Riemann sample rules, sampled cell
    statistics, explicit domain indicators, refinement tables and prism views.
    Samples standalone planar regions with reusable strip grids and separate
    filled-domain or horizontal-plate displays. Samples six faces of nested
    Cartesian solids with shared endpoints and independent face/wireframe
    displays, without coupling geometric sampling to quadrature. Maps stored
    cylindrical parameter patches into Cartesian walls, caps and angular cuts
    with explicit seam and axis-degeneracy limitations. Samples spherical
    radial shells and angular cuts with explicit pole/origin degeneracies
    and separate stored-face displays. Shows stored stationary candidates
    on sampled scalar graphs without rerunning search or classification.
    Samples spatial parametric curves, displays stored samples, and integrates
    speed using supplied velocities or numerical Jacobians. Computes spatial
    Frenet directions, curvature and signed torsion with derivative diagnostics
    and displays stored results. Samples osculating circles and ribbons
    with explicit geometry gaps and separate interactive views. Samples
    spatial vector fields, estimates divergence and curl, and integrates
    streamlines or time-dependent pathlines with fixed-step Runge-Kutta.
    Computes signed scalar line integrals and oriented vector work in two
    and three dimensions, with separate quadrature and derivative diagnostics.
    Samples parametric and ruled surfaces and integrates scalar densities,
    area and oriented flux over rectangular parameter domains. Compares
    the two integrals in Green's circulation theorem over a planar strip
    and in Stokes' theorem over a rectangular parameter patch. Compares
    outward flux and integrated divergence over a Cartesian box.
License: MIT + file LICENSE
Depends: R (>= 4.1.0)
Imports: stats
Suggests: testthat (>= 3.0.0), plotly
Config/testthat/edition: 3
Encoding: UTF-8
Config/roxygen2/version: 8.1.0
Author: Julio Lizarazo Osorio [aut],
  Julian Mauricio Fajardo [aut, cre]
Maintainer: Julian Mauricio Fajardo <julian.fajardo1908@gmail.com>
URL: https://github.com/JulianFajardo1908/vectorialcalculus
BugReports: https://github.com/JulianFajardo1908/vectorialcalculus/issues
NeedsCompilation: no
Packaged: 2026-11-10 00:39:40 UTC; LENOVO
Repository: CRAN
Date/Publication: 2026-11-10 09:30:08 UTC
