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vectorialcalculus (version 1.0.5)

Vector Calculus Tools for Visualization and Analysis

Description

Provides pedagogical tools for visualization and numerical computation in vector calculus. Includes functions for parametric curves, scalar and vector fields, gradients, divergences, curls, line and surface integrals, and dynamic 2D/3D graphical analysis to support teaching and learning. The implemented methods follow standard treatments in vector calculus and multivariable analysis as presented in Marsden and Tromba (2011) , Stewart (2015) , Thomas, Weir and Hass (2018) , Larson and Edwards (2016) , Apostol (1969) , Spivak (1971) , Schey (2005) , Colley (2019) , Lizarazo Osorio (2020) , Sievert (2020) , and Borowko (2013) .

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install.packages('vectorialcalculus')

Version

1.0.5

License

MIT + file LICENSE

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Repository

https://github.com/JulianFajardo1908/vectorialcalculus

Maintainer

Julian Mauricio Fajardo

Last Published

January 19th, 2026

Functions in vectorialcalculus (1.0.5)

integrate_double_xy

Unified Numerical Double Integration

line_integral2d

Line integral of a scalar field along a planar curve, with optional 3D visualization

Optimality check with Lagrange multipliers and bordered Hessian

line_integral_vector2d

2D line integral of a vector field with visualization

integrate_double_polar

Numerical Double Integration in Polar Coordinates

line_integral3d_work

3D line integral with work visualization

Frenet-Serret frame for a 3D parametric curve

gradient_direction2d

Animate gradient and directional derivative on level curves (2D)

gradient_scalar

Gradient of a scalar field in R^n

integrate_triple_general

Numerical Triple Integration over a General Region

newton_raphson2d

Newton-Raphson method for systems in R^2 with animation (Plotly)

Plot a 3D parametric curve with plotly

plot_surface_with_tangents

Surface with tangent lines at a point

Principal normal vectors along a 3D curve

osculating_circle3d

Osculating discs and circles of a spatial curve

Planar region \(\{(x, y): a \leq x \leq b, H1(x) \leq y \leq H2(x)\}\) drawn at height z0

related_rates_grad

Related rates via the gradient (implicit constraint)

osculating_ribbon3d

Osculating ribbon along a 3D parametric curve

partial_derivatives_surface

Partial derivatives of z = f(x, y) at a point with 3D visualization

newton_raphson_anim

Newton-Raphson root finding with tangent animation (Plotly)

Secant lines converge to the tangent line (Plotly)

Solid defined by bounds in x, y and z

solid_of_revolution_y

Solid of revolution around a horizontal line

streamline_and_field3d

Vector field and streamline in 3D (single combined figure)

riemann_sum_1d_plot

1D Riemann sums with optional plot

riemann_sum_2d_plot

2D Riemann sums (upper, lower, midpoint) with a 3D plot

solid_spherical3d

Solid in spherical coordinates with Plotly visualization and volume

riemann_prisms3d

Riemann rectangular prisms over a planar region

riemann_rectangles2d

Animate Riemann rectangles under a curve (2D)

solid_cylindrical3d

Cylindrical solid defined by radial and vertical bounds (with optional plot)

3D vector field in a curvilinear prism

Planar region between two curves y = H1(x) and y = H2(x)

surface_integral_z

Surface integral over a graph z = g(x, y)

Unit tangent vectors along a 3D parametric curve

total_differential_nd

Total differential of a scalar field in R^n

tangent_plane3d

Tangent plane and normal vector to a surface z = f(x, y)

surface_parametric_area

Plot a parametric surface and estimate its area

Sample a 3D parametric curve

critical_points_2d

Critical points of a two-variable function using gradient and Hessian

Binormal vectors along a 3D parametric curve

curvature_torsion3d

Curvature and torsion of a 3D parametric curve

Numerical curl of a three-dimensional vector field

cylindrical_surface3d

Ruled surface along a 3D parametric curve

directional_derivative3d

Directional derivative in any dimension, with optional 2D visualization

divergence_field

Numerical divergence of a vector field

critical_points_nd

Critical points of a scalar field in n dimensions (no plot)

Numeric arc length of a 3D parametric curve