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<h1 class="quarto-secondary-nav-title"><span class="chapter-number">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></h1>
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<a href="../limits/limits_extensions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">19</span> <span class="chapter-title">Limits, issues, extensions of the concept</span></a>
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<a href="../limits/continuity.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">20</span> <span class="chapter-title">Continuity</span></a>
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<a href="../limits/intermediate_value_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">21</span> <span class="chapter-title">Implications of continuity</span></a>
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<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-3" aria-expanded="false">Derivatives</a>
|
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<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-3" aria-expanded="false">
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<a href="../derivatives/derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">22</span> <span class="chapter-title">Derivatives</span></a>
|
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<a href="../derivatives/numeric_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">23</span> <span class="chapter-title">Numeric derivatives</span></a>
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<a href="../derivatives/symbolic_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">24</span> <span class="chapter-title">Symbolic derivatives</span></a>
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<a href="../derivatives/mean_value_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">25</span> <span class="chapter-title">The mean value theorem for differentiable functions.</span></a>
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<a href="../derivatives/optimization.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">26</span> <span class="chapter-title">Optimization</span></a>
|
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<a href="../derivatives/first_second_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">27</span> <span class="chapter-title">The first and second derivatives</span></a>
|
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<a href="../derivatives/curve_sketching.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">28</span> <span class="chapter-title">Curve Sketching</span></a>
|
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|
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<a href="../derivatives/linearization.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">29</span> <span class="chapter-title">Linearization</span></a>
|
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</div>
|
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<a href="../derivatives/newtons_method.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">30</span> <span class="chapter-title">Newton’s method</span></a>
|
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</div>
|
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|||
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<a href="../derivatives/more_zeros.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">31</span> <span class="chapter-title">Derivative-free alternatives to Newton’s method</span></a>
|
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</div>
|
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|
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<li class="sidebar-item">
|
|||
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|
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<a href="../derivatives/lhospitals_rule.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">32</span> <span class="chapter-title">L’Hospital’s Rule</span></a>
|
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</div>
|
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|
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|
|||
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|
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<a href="../derivatives/implicit_differentiation.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">33</span> <span class="chapter-title">Implicit Differentiation</span></a>
|
|||
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</div>
|
|||
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</li>
|
|||
|
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|
|||
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|
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<a href="../derivatives/related_rates.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">34</span> <span class="chapter-title">Related rates</span></a>
|
|||
|
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</div>
|
|||
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|
|||
|
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|
|||
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|
|||
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|
<a href="../derivatives/taylor_series_polynomials.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">35</span> <span class="chapter-title">Taylor Polynomials and other Approximating Polynomials</span></a>
|
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</div>
|
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|
|||
|
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</ul>
|
|||
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|
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|||
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|
|||
|
|
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-4" aria-expanded="false">Integrals</a>
|
|||
|
|
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-4" aria-expanded="false">
|
|||
|
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<i class="bi bi-chevron-right ms-2"></i>
|
|||
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|
|||
|
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|
|||
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|
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|
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|
|||
|
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<a href="../integrals/area.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">36</span> <span class="chapter-title">Area under a curve</span></a>
|
|||
|
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</div>
|
|||
|
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|
|||
|
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|||
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|
|||
|
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<a href="../integrals/ftc.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">37</span> <span class="chapter-title">Fundamental Theorem or Calculus</span></a>
|
|||
|
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</div>
|
|||
|
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</li>
|
|||
|
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|
|||
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|
|||
|
|
<a href="../integrals/substitution.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">38</span> <span class="chapter-title">Substitution</span></a>
|
|||
|
|
</div>
|
|||
|
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</li>
|
|||
|
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|
|||
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|
|||
|
|
<a href="../integrals/integration_by_parts.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">39</span> <span class="chapter-title">Integration By Parts</span></a>
|
|||
|
|
</div>
|
|||
|
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|
|||
|
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|
|||
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|
|||
|
|
<a href="../integrals/partial_fractions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">40</span> <span class="chapter-title">Partial Fractions</span></a>
|
|||
|
|
</div>
|
|||
|
|
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|
|||
|
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|
|||
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|
|||
|
|
<a href="../integrals/improper_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">41</span> <span class="chapter-title">Improper Integrals</span></a>
|
|||
|
|
</div>
|
|||
|
|
</li>
|
|||
|
|
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|
|||
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|
|||
|
|
<a href="../integrals/mean_value_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">42</span> <span class="chapter-title">Mean value theorem for integrals</span></a>
|
|||
|
|
</div>
|
|||
|
|
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|
|||
|
|
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|
|||
|
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|
|||
|
|
<a href="../integrals/area_between_curves.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">43</span> <span class="chapter-title">Area between two curves</span></a>
|
|||
|
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</div>
|
|||
|
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|
|||
|
|
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|
|||
|
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|
|||
|
|
<a href="../integrals/center_of_mass.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">44</span> <span class="chapter-title">Center of Mass</span></a>
|
|||
|
|
</div>
|
|||
|
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|
|||
|
|
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|
|||
|
|
<div class="sidebar-item-container">
|
|||
|
|
<a href="../integrals/volumes_slice.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">45</span> <span class="chapter-title">Volumes by slicing</span></a>
|
|||
|
|
</div>
|
|||
|
|
</li>
|
|||
|
|
<li class="sidebar-item">
|
|||
|
|
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|
|||
|
|
<a href="../integrals/arc_length.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">46</span> <span class="chapter-title">Arc length</span></a>
|
|||
|
|
</div>
|
|||
|
|
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|
|||
|
|
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|
|||
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|
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|
|||
|
|
<a href="../integrals/surface_area.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">47</span> <span class="chapter-title">Surface Area</span></a>
|
|||
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</div>
|
|||
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|
|||
|
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</ul>
|
|||
|
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|
|||
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|
|||
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|
|||
|
|
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-5" aria-expanded="false">ODEs</a>
|
|||
|
|
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-5" aria-expanded="false">
|
|||
|
|
<i class="bi bi-chevron-right ms-2"></i>
|
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|
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|
|||
|
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|
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|
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|
|
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|
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|
|||
|
|
<a href="../ODEs/odes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">48</span> <span class="chapter-title">ODEs</span></a>
|
|||
|
|
</div>
|
|||
|
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|
|||
|
|
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|
|||
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|
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|
|||
|
|
<a href="../ODEs/euler.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">49</span> <span class="chapter-title">Euler’s method</span></a>
|
|||
|
|
</div>
|
|||
|
|
</li>
|
|||
|
|
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|
|||
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|
|||
|
|
<a href="../ODEs/solve.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">50</span> <span class="chapter-title">The problem-algorithm-solve interface</span></a>
|
|||
|
|
</div>
|
|||
|
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</li>
|
|||
|
|
<li class="sidebar-item">
|
|||
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|
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|
|||
|
|
<a href="../ODEs/differential_equations.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">51</span> <span class="chapter-title">The <code>DifferentialEquations</code> suite</span></a>
|
|||
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|
|||
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|
|||
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|
|||
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|||
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|||
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|
|||
|
|
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-6" aria-expanded="false">Differential vector calculus</a>
|
|||
|
|
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-6" aria-expanded="false">
|
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|
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|
|||
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|
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|
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|
|||
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|
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|
|||
|
|
<a href="../differentiable_vector_calculus/polar_coordinates.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">52</span> <span class="chapter-title">Polar Coordinates and Curves</span></a>
|
|||
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|
|||
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|
|||
|
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|
|||
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|
|||
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|
<a href="../differentiable_vector_calculus/vectors.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">53</span> <span class="chapter-title">Vectors and matrices</span></a>
|
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|
|||
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|
|||
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|
|||
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|
|||
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|
<a href="../differentiable_vector_calculus/vector_valued_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">54</span> <span class="chapter-title">Vector-valued functions, <span class="math inline">\(f:R \rightarrow R^n\)</span></span></a>
|
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</div>
|
|||
|
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|
|||
|
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|||
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|
|||
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|
<a href="../differentiable_vector_calculus/scalar_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">55</span> <span class="chapter-title">Scalar functions</span></a>
|
|||
|
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</div>
|
|||
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|
|||
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|
|||
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|
|||
|
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<a href="../differentiable_vector_calculus/scalar_functions_applications.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">56</span> <span class="chapter-title">Applications with scalar functions</span></a>
|
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|
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</div>
|
|||
|
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|
|||
|
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<li class="sidebar-item">
|
|||
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|
|||
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|
<a href="../differentiable_vector_calculus/vector_fields.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">57</span> <span class="chapter-title">Functions <span class="math inline">\(R^n \rightarrow R^m\)</span></span></a>
|
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</div>
|
|||
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|
|||
|
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<li class="sidebar-item">
|
|||
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|
|||
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|
<a href="../differentiable_vector_calculus/plots_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">58</span> <span class="chapter-title">2D and 3D plots in Julia with Plots</span></a>
|
|||
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|
|||
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|
|||
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|
|||
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|
|||
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|||
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|
|||
|
|
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-7" aria-expanded="false">Integral vector calculus</a>
|
|||
|
|
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-7" aria-expanded="false">
|
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<i class="bi bi-chevron-right ms-2"></i>
|
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|
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|
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|
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|
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|
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|
|
<a href="../integral_vector_calculus/double_triple_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">59</span> <span class="chapter-title">Multi-dimensional integrals</span></a>
|
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|
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|
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|
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|
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|
|||
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|
<a href="../integral_vector_calculus/line_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">60</span> <span class="chapter-title">Line and Surface Integrals</span></a>
|
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|
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</div>
|
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|
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|
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<a href="../integral_vector_calculus/div_grad_curl.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">61</span> <span class="chapter-title">The Gradient, Divergence, and Curl</span></a>
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<a href="../integral_vector_calculus/stokes_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">62</span> <span class="chapter-title">Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem</span></a>
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<a href="../integral_vector_calculus/review.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">63</span> <span class="chapter-title">Quick Review of Vector Calculus</span></a>
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<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-8" aria-expanded="false">Alternatives</a>
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<a href="../alternatives/plotly_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">64</span> <span class="chapter-title">JavaScript based plotting libraries</span></a>
|
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<a href="../alternatives/makie_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">65</span> <span class="chapter-title">Calculus plots with Makie</span></a>
|
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<a href="../misc/getting_started_with_julia.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">66</span> <span class="chapter-title">Getting started with Julia</span></a>
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<a href="../misc/julia_interfaces.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">67</span> <span class="chapter-title">Julia interfaces</span></a>
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<a href="../misc/calculus_with_julia.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></a>
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<a href="../misc/unicode.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">69</span> <span class="chapter-title">Usages of Unicode symbols</span></a>
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<a href="../misc/quick_notes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">70</span> <span class="chapter-title">Quick introduction to Calculus with Julia</span></a>
|
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<a href="../references.html" class="sidebar-item-text sidebar-link">References</a>
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<h2 id="toc-title">Table of contents</h2>
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<li><a href="#the-package-concept" id="toc-the-package-concept" class="nav-link active" data-scroll-target="#the-package-concept"> <span class="header-section-number">68.1</span> The package concept</a>
|
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|
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<li><a href="#package-installation" id="toc-package-installation" class="nav-link" data-scroll-target="#package-installation"> <span class="header-section-number">68.1.1</span> Package installation</a></li>
|
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<li><a href="#using-a-package" id="toc-using-a-package" class="nav-link" data-scroll-target="#using-a-package"> <span class="header-section-number">68.1.2</span> Using a package</a></li>
|
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<li><a href="#package-details" id="toc-package-details" class="nav-link" data-scroll-target="#package-details"> <span class="header-section-number">68.1.3</span> Package details</a></li>
|
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|
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<div class="toc-actions"><div><i class="bi bi-github"></i></div><div class="action-links"><p><a href="https://github.com/jverzani/CalculusWithJuliaNotes.jl/edit/main/quarto/misc/calculus_with_julia.qmd" class="toc-action">Edit this page</a></p><p><a href="https://github.com/jverzani/CalculusWithJuliaNotes.jl/issues/new" class="toc-action">Report an issue</a></p></div></div></nav>
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|
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<h1 class="title d-none d-lg-block"><span class="chapter-number">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></h1>
|
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</header>
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|
|||
|
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<p>To run the commands in these notes, some external packages must be installed and loaded.</p>
|
|||
|
|
<p>The <code>Pluto</code> interface does this in the background, so there is nothing to do but execute the cells that call <code>using</code> or <code>import</code>. For <code>Julia</code> post version <code>1.7</code>, this installation will be initiated for you when <code>using</code> is called in the REPL terminal.</p>
|
|||
|
|
<p>For other interfaces, to use the <code>CalculusWithJulia</code> package requires first that it be installed. From the command line. This can be done with this key sequence:</p>
|
|||
|
|
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>] add CalculusWithJulia</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
|||
|
|
<p>Or, using the <code>Pkg</code> package, the commands would be</p>
|
|||
|
|
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> <span class="bu">Pkg</span></span>
|
|||
|
|
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="bu">Pkg</span>.<span class="fu">add</span>(<span class="st">"CalculusWithJulia"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
|||
|
|
<p>Installation only needs to be done once.</p>
|
|||
|
|
<hr>
|
|||
|
|
<p>However, for each new <code>Julia</code> session, the package must be <em>loaded</em>, as with the following command:</p>
|
|||
|
|
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">CalculusWithJulia</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
|||
|
|
<p>That is all. The rest of this page just provides some details for the interested reader.</p>
|
|||
|
|
<section id="the-package-concept" class="level2" data-number="68.1">
|
|||
|
|
<h2 data-number="68.1" class="anchored" data-anchor-id="the-package-concept"><span class="header-section-number">68.1</span> The package concept</h2>
|
|||
|
|
<p>The <code>Julia</code> language provides the building blocks for the wider <code>Julia</code> ecosystem that enhance and extend the language’s applicability.</p>
|
|||
|
|
<p><code>Julia</code> is extended through “packages.” Some of these, such as packages for certain math constants and some linear algebra operations, are part of all <code>Julia</code> installations and must simple by loaded to be used. Others, such as packages for finding integrals or (automatic) derivatives are provided by users and must first be <em>installed</em> before being used.</p>
|
|||
|
|
<section id="package-installation" class="level3" data-number="68.1.1">
|
|||
|
|
<h3 data-number="68.1.1" class="anchored" data-anchor-id="package-installation"><span class="header-section-number">68.1.1</span> Package installation</h3>
|
|||
|
|
<p>Package installation is straightforward, as <code>Julia</code> has a package, <code>Pkg</code>, that facilitates this.</p>
|
|||
|
|
<p>Since <code>Julia</code> version 1.7, just attempting to load a package through <code>using PackageName</code> at the <em>command line</em> will either load an installed package <em>or</em> query for an uninstalled package to be installed before lading. So installation just requires confirming a prompt.</p>
|
|||
|
|
<p>For more control, the command line and <code>IJulia</code> provide access to the function in <code>Pkg</code> through the escape command <code>]</code>. For example, to find the status of all currently installed packages, the following command can be executed:</p>
|
|||
|
|
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>] status</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
|||
|
|
<p>External packages are <em>typically</em> installed from GitHub and if they are regisered, installation is as easy as calling <code>add</code>:</p>
|
|||
|
|
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>] add QuadGK</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
|||
|
|
<p>That command will consult <code>Julia</code>’s general registry for the location of the <code>QuadGK</code> package, use this location to download the necessary files, if necessary dependencies will be built and installed, and then the package available for use.</p>
|
|||
|
|
<p>For these notes, when the <code>CalculusWithJulia</code> package is installed it will also install many of the other packages that are needed.</p>
|
|||
|
|
<p>See <a href="https://docs.julialang.org/en/v1/stdlib/Pkg/index.html">Pkg</a> for more details, such as how to update the set of available packages.</p>
|
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</section>
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<section id="using-a-package" class="level3" data-number="68.1.2">
|
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<h3 data-number="68.1.2" class="anchored" data-anchor-id="using-a-package"><span class="header-section-number">68.1.2</span> Using a package</h3>
|
|||
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<p>The features of an installed package are not available until the package is brought into the current session. A package need only be <em>installed</em> once, but must be loaded each session.</p>
|
|||
|
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<p>To load a package, the <code>using</code> keyword is provided:</p>
|
|||
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<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">QuadGK</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
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<p>The above command will make available all <em>exported</em> function names from the <code>QuadGK</code> package so they can be directly used, as in:</p>
|
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<div class="cell" data-execution_count="9">
|
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<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">quadgk</span>(sin, <span class="fl">0</span>, <span class="cn">pi</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
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<div class="cell-output cell-output-display" data-execution_count="6">
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<pre><code>(2.0, 1.7905676941154525e-12)</code></pre>
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</div>
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</div>
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<p>(A command to find an integral of <span class="math inline">\(f(x) = \sin(x)\)</span> over <span class="math inline">\([0, \pi]\)</span>.)</p>
|
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</section>
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<section id="package-details" class="level3" data-number="68.1.3">
|
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<h3 data-number="68.1.3" class="anchored" data-anchor-id="package-details"><span class="header-section-number">68.1.3</span> Package details</h3>
|
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<p>When a package is <em>first</em> loaded after installation, or some other change, it will go through a <em>pre-compilation</em> process. Depending on the package size, this can take a moment to several seconds. This won’t happen the second time a package is loaded.</p>
|
|||
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<p>However, subsequent times a package is loaded some further compilation is done, so it can still take some time for a package to load. Mostly this is not noticeable, though with the plotting package used in these notes, it is.</p>
|
|||
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<p>When a package is loaded, all of its dependent packages are also loaded, but their functions are not immediately available to the user.</p>
|
|||
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<p>In <em>typical</em> <code>Julia</code> usage, each needed package is loaded on demand. This is faster and also keeps the namespace (the collection of variable and function names) smaller to avoid collisions. However, for these notes, the package <code>CalculusWithJulia</code> will load a few of the packages needed for the entire set of notes, not just the current section. This is to make it a bit <em>easier</em> for the <em>beginning</em> user.</p>
|
|||
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<p>One issue with loading several packages is the possibility that more than one will export a function with the same name, causing a collision. Moreover, at times, there can be dependency conflicts between packages. A suggested workflow is to use projects and in each project use a minimal set of packages. In Pluto, this is done behind the scenes.</p>
|
|||
|
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<p>The <code>Julia</code> language is designed around have several “generic” functions each with many different methods depending on their usage. This design allows many different implementations for operations such as addition or multiplication yet the user only needs to call one function name. Packages can easily extend these generic functions by providing their own methods for their own new types of data. For example, <code>SymPy</code>, which adds symbolic math features to <code>Julia</code> (using a Python package) extends both <code>+</code> and <code>*</code> for use with symbolic objects.</p>
|
|||
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<p>This design works great when the “generic” usage matches the needs of the package authors, but there are two common issues that arise:</p>
|
|||
|
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<ul>
|
|||
|
|
<li>The extension of a generic is for a type defined outside the author’s package. This is known as “type piracy” and is frowned on, as it can lead to subtle errors. The <code>CalculusWithJulia</code> package practices this for one case: using <code>'</code> to indicate derivatives for <code>Function</code> objects.</li>
|
|||
|
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<li>The generic function concept is not part of base <code>Julia</code>. An example might be the <code>solve</code> function. This name has a well-defined mathematical usage (e.g., “solve for <span class="math inline">\(x\)</span>.”), but the generic concept is not part of base <code>Julia</code>. As it is used by <code>SymPy</code> and <code>DifferentialEquations</code>, among others, the ecosystem has a stub package <code>CommonSolve</code> allowing the sharing of this “verb.”</li>
|
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|
|||
|
|
var currentTitle = button.getAttribute("title");
|
|||
|
|
button.setAttribute("title", "Copied!");
|
|||
|
|
setTimeout(function() {
|
|||
|
|
button.setAttribute("title", currentTitle);
|
|||
|
|
button.classList.remove('code-copy-button-checked');
|
|||
|
|
}, 1000);
|
|||
|
|
// clear code selection
|
|||
|
|
e.clearSelection();
|
|||
|
|
});
|
|||
|
|
function tippyHover(el, contentFn) {
|
|||
|
|
const config = {
|
|||
|
|
allowHTML: true,
|
|||
|
|
content: contentFn,
|
|||
|
|
maxWidth: 500,
|
|||
|
|
delay: 100,
|
|||
|
|
arrow: false,
|
|||
|
|
appendTo: function(el) {
|
|||
|
|
return el.parentElement;
|
|||
|
|
},
|
|||
|
|
interactive: true,
|
|||
|
|
interactiveBorder: 10,
|
|||
|
|
theme: 'quarto',
|
|||
|
|
placement: 'bottom-start'
|
|||
|
|
};
|
|||
|
|
window.tippy(el, config);
|
|||
|
|
}
|
|||
|
|
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
|
|||
|
|
for (var i=0; i<noterefs.length; i++) {
|
|||
|
|
const ref = noterefs[i];
|
|||
|
|
tippyHover(ref, function() {
|
|||
|
|
let href = ref.getAttribute('href');
|
|||
|
|
try { href = new URL(href).hash; } catch {}
|
|||
|
|
const id = href.replace(/^#\/?/, "");
|
|||
|
|
const note = window.document.getElementById(id);
|
|||
|
|
return note.innerHTML;
|
|||
|
|
});
|
|||
|
|
}
|
|||
|
|
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
|
|||
|
|
for (var i=0; i<bibliorefs.length; i++) {
|
|||
|
|
const ref = bibliorefs[i];
|
|||
|
|
const cites = ref.parentNode.getAttribute('data-cites').split(' ');
|
|||
|
|
tippyHover(ref, function() {
|
|||
|
|
var popup = window.document.createElement('div');
|
|||
|
|
cites.forEach(function(cite) {
|
|||
|
|
var citeDiv = window.document.createElement('div');
|
|||
|
|
citeDiv.classList.add('hanging-indent');
|
|||
|
|
citeDiv.classList.add('csl-entry');
|
|||
|
|
var biblioDiv = window.document.getElementById('ref-' + cite);
|
|||
|
|
if (biblioDiv) {
|
|||
|
|
citeDiv.innerHTML = biblioDiv.innerHTML;
|
|||
|
|
}
|
|||
|
|
popup.appendChild(citeDiv);
|
|||
|
|
});
|
|||
|
|
return popup.innerHTML;
|
|||
|
|
});
|
|||
|
|
}
|
|||
|
|
var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//);
|
|||
|
|
var filterRegex = new RegExp('/' + window.location.host + '/');
|
|||
|
|
var isInternal = (href) => {
|
|||
|
|
return filterRegex.test(href) || localhostRegex.test(href);
|
|||
|
|
}
|
|||
|
|
// Inspect non-navigation links and adorn them if external
|
|||
|
|
var links = window.document.querySelectorAll('a:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external)');
|
|||
|
|
for (var i=0; i<links.length; i++) {
|
|||
|
|
const link = links[i];
|
|||
|
|
if (!isInternal(link.href)) {
|
|||
|
|
// target, if specified
|
|||
|
|
link.setAttribute("target", "_blank");
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
});
|
|||
|
|
</script>
|
|||
|
|
<nav class="page-navigation">
|
|||
|
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<div class="nav-page nav-page-previous">
|
|||
|
|
<a href="../misc/julia_interfaces.html" class="pagination-link">
|
|||
|
|
<i class="bi bi-arrow-left-short"></i> <span class="nav-page-text"><span class="chapter-number">67</span> <span class="chapter-title">Julia interfaces</span></span>
|
|||
|
|
</a>
|
|||
|
|
</div>
|
|||
|
|
<div class="nav-page nav-page-next">
|
|||
|
|
<a href="../misc/unicode.html" class="pagination-link">
|
|||
|
|
<span class="nav-page-text"><span class="chapter-number">69</span> <span class="chapter-title">Usages of Unicode symbols</span></span> <i class="bi bi-arrow-right-short"></i>
|
|||
|
|
</a>
|
|||
|
|
</div>
|
|||
|
|
</nav>
|
|||
|
|
</div> <!-- /content -->
|
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|
|
<footer class="footer">
|
|||
|
|
<div class="nav-footer">
|
|||
|
|
<div class="nav-footer-center">Copyright 2022, John Verzani</div>
|
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|
|
</div>
|
|||
|
|
</footer>
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
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|
|
</body></html>
|