divergence_field

Computes the divergence of a vector field at a given point using
central finite differences. The vector field <code>field</code> must take a
numeric vector <code>x</code> and return a numeric vector of the same length.

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) <ISBN:9781429215084>, Stewart (2015) <ISBN:9781285741550>, Thomas, Weir and Hass (2018) <ISBN:9780134438986>, Larson and Edwards (2016) <ISBN:9781285255869>, Apostol (1969) <ISBN:9780471000051>, Spivak (1971) <ISBN:9780805390216>, Schey (2005) <ISBN:9780071369080>, Colley (2019) <ISBN:9780321982384>, Lizarazo Osorio (2020) <ISBN:9789585450103>, Sievert (2020) <ISBN:9780367180165>, and Borowko (2013) <ISBN:9781439870791>.

Julian Mauricio Fajardo

vectorialcalculus

Vector Calculus Tools for Visualization and Analysis

Julio Lizarazo Osorio

divergence_field function

<dl><dt>field</dt>
<dd>Function of the form <code>field(x)</code> returning a numeric vector
of the same length as <code>x</code>.</dd>
<dt>x0</dt>
<dd>Numeric vector giving the evaluation point.</dd>
<dt>h</dt>
<dd>Step size for finite differences. Can be:<ul>
<li><code>NULL</code>: an automatic step is selected as
<code>1e-4 * (1 + abs(x0))</code>;</li>
<li>A numeric scalar: same step for all components;</li>
<li>A numeric vector of the same length as <code>x0</code>.</li>
</ul></dd>
<dt>plot</dt>
<dd>Logical; if <code>TRUE</code> and the dimension is 2 or 3,
a basic visualization is drawn with plotly.</dd></dl>

Arguments

Numerical divergence of a vector field — divergence_field

<dl>

<dt>field</dt>
<dd>Function of the form <code>field(x)</code> returning a numeric vector
of the same length as <code>x</code>.</dd>


<dt>x0</dt>
<dd>Numeric vector giving the evaluation point.</dd>


<dt>h</dt>
<dd>Step size for finite differences. Can be:<ul>
<li><code>NULL</code>: an automatic step is selected as
<code>1e-4 * (1 + abs(x0))</code>;</li>
<li>A numeric scalar: same step for all components;</li>
<li>A numeric vector of the same length as <code>x0</code>.</li>
</ul></dd>


<dt>plot</dt>
<dd>Logical; if <code>TRUE</code> and the dimension is 2 or 3,
a basic visualization is drawn with plotly.</dd>

</dl>

divergence_field: Numerical divergence of a vector field

Description

Usage

Value

Arguments

Details

Examples