Vector Calculus Tools for Visualization and Analysis

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Documentation for package ‘vectorialcalculus’ version 1.0.5

Help Pages

arc_length3d Numeric arc length of a 3D parametric curve
binormal3d Binormal vectors along a 3D parametric curve
critical_points_2d Critical points of a two-variable function using gradient and Hessian
critical_points_nd Critical points of a scalar field in n dimensions (no plot)
curl3d Numerical curl of a three-dimensional vector field
curvature_torsion3d Curvature and torsion of a 3D parametric curve
curve_sample3d Sample a 3D parametric curve
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
frenet_frame3d 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_double_polar Numerical Double Integration in Polar Coordinates
integrate_double_xy Unified Numerical Double Integration
integrate_triple_general Numerical Triple Integration over a General Region
lagrange_check Optimality check with Lagrange multipliers and bordered Hessian
line_integral2d Line integral of a scalar field along a planar curve, with optional 3D visualization
line_integral3d_work 3D line integral with work visualization
line_integral_vector2d 2D line integral of a vector field with visualization
newton_raphson2d Newton-Raphson method for systems in R^2 with animation (Plotly)
newton_raphson_anim Newton-Raphson root finding with tangent animation (Plotly)
normal3d Principal normal vectors along a 3D curve
osculating_circle3d Osculating discs and circles of a spatial curve
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
plot_curve3d Plot a 3D parametric curve with plotly
plot_surface_with_tangents Surface with tangent lines at a point
region_xyz0 Planar region \{(x, y): a <=q x <=q b, H1(x) <=q y <=q H2(x)\} drawn at height z0
related_rates_grad Related rates via the gradient (implicit constraint)
riemann_prisms3d Riemann rectangular prisms over a planar region
riemann_rectangles2d Animate Riemann rectangles under a curve (2D)
riemann_sum_1d_plot 1D Riemann sums with optional plot
riemann_sum_2d_plot 2D Riemann sums (upper, lower, midpoint) with a 3D plot
secant_tangent Secant lines converge to the tangent line (Plotly)
solid_cylindrical3d Cylindrical solid defined by radial and vertical bounds (with optional plot)
solid_of_revolution_y Solid of revolution around a horizontal line
solid_spherical3d Solid in spherical coordinates with Plotly visualization and volume
solid_xyz3d Solid defined by bounds in x, y and z
streamline_and_field3d Vector field and streamline in 3D (single combined figure)
surface_integral_z Surface integral over a graph z = g(x, y)
surface_parametric_area Plot a parametric surface and estimate its area
tangent3d Unit tangent vectors along a 3D parametric curve
tangent_plane3d Tangent plane and normal vector to a surface z = f(x, y)
total_differential_nd Total differential of a scalar field in R^n
vector_field3d 3D vector field in a curvilinear prism
xy_region Planar region between two curves y = H1(x) and y = H2(x)