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<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-1" aria-expanded="false">Precalculus Concepts</a>
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<a href="./precalc/calculator.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">1</span>&nbsp; <span class="chapter-title">From calculator to computer</span></a>
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<a href="./precalc/variables.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">2</span>&nbsp; <span class="chapter-title">Variables</span></a>
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<a href="./precalc/numbers_types.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Number systems</span></a>
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<a href="./precalc/logical_expressions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">4</span>&nbsp; <span class="chapter-title">Inequalities, Logical expressions</span></a>
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<a href="./precalc/vectors.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">5</span>&nbsp; <span class="chapter-title">Vectors</span></a>
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<a href="./precalc/ranges.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">6</span>&nbsp; <span class="chapter-title">Ranges and Sets</span></a>
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<a href="./precalc/functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">7</span>&nbsp; <span class="chapter-title">Functions</span></a>
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<a href="./precalc/plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">8</span>&nbsp; <span class="chapter-title">The Graph of a Function</span></a>
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<a href="./precalc/transformations.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">9</span>&nbsp; <span class="chapter-title">Function manipulations</span></a>
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<a href="./precalc/inversefunctions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">10</span>&nbsp; <span class="chapter-title">The Inverse of a Function</span></a>
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<a href="./precalc/polynomial.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">11</span>&nbsp; <span class="chapter-title">Polynomials</span></a>
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<a href="./precalc/polynomial_roots.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">12</span>&nbsp; <span class="chapter-title">Roots of a polynomial</span></a>
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<a href="./precalc/rational_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">14</span>&nbsp; <span class="chapter-title">Rational functions</span></a>
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<a href="./precalc/exp_log_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">15</span>&nbsp; <span class="chapter-title">Exponential and logarithmic functions</span></a>
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<a href="./precalc/trig_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">16</span>&nbsp; <span class="chapter-title">Trigonometric functions</span></a>
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<a href="./precalc/julia_overview.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">17</span>&nbsp; <span class="chapter-title">Overview of Julia commands</span></a>
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<a href="./limits/limits_extensions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">19</span>&nbsp; <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>&nbsp; <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>&nbsp; <span class="chapter-title">Implications of continuity</span></a>
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<a href="./derivatives/numeric_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">23</span>&nbsp; <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>&nbsp; <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>&nbsp; <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>&nbsp; <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>&nbsp; <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>&nbsp; <span class="chapter-title">Curve Sketching</span></a>
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<a href="./derivatives/linearization.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">29</span>&nbsp; <span class="chapter-title">Linearization</span></a>
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<a href="./derivatives/newtons_method.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">30</span>&nbsp; <span class="chapter-title">Newtons method</span></a>
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<a href="./derivatives/more_zeros.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">31</span>&nbsp; <span class="chapter-title">Derivative-free alternatives to Newtons method</span></a>
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<a href="./derivatives/lhospitals_rule.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">32</span>&nbsp; <span class="chapter-title">LHospitals Rule</span></a>
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<a href="./derivatives/implicit_differentiation.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">33</span>&nbsp; <span class="chapter-title">Implicit Differentiation</span></a>
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<a href="./derivatives/related_rates.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">34</span>&nbsp; <span class="chapter-title">Related rates</span></a>
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<a href="./derivatives/taylor_series_polynomials.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">35</span>&nbsp; <span class="chapter-title">Taylor Polynomials and other Approximating Polynomials</span></a>
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<a href="./integrals/area.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">36</span>&nbsp; <span class="chapter-title">Area under a curve</span></a>
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<a href="./integrals/ftc.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">37</span>&nbsp; <span class="chapter-title">Fundamental Theorem or Calculus</span></a>
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<a href="./integrals/substitution.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">38</span>&nbsp; <span class="chapter-title">Substitution</span></a>
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<a href="./integrals/integration_by_parts.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">39</span>&nbsp; <span class="chapter-title">Integration By Parts</span></a>
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<a href="./integrals/mean_value_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">42</span>&nbsp; <span class="chapter-title">Mean value theorem for integrals</span></a>
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<a href="./integrals/area_between_curves.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">43</span>&nbsp; <span class="chapter-title">Area between two curves</span></a>
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<a href="./integrals/center_of_mass.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">44</span>&nbsp; <span class="chapter-title">Center of Mass</span></a>
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<a href="./integrals/volumes_slice.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">45</span>&nbsp; <span class="chapter-title">Volumes by slicing</span></a>
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<a href="./integrals/arc_length.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">46</span>&nbsp; <span class="chapter-title">Arc length</span></a>
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<a href="./integrals/surface_area.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">47</span>&nbsp; <span class="chapter-title">Surface Area</span></a>
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<a href="./ODEs/odes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">48</span>&nbsp; <span class="chapter-title">ODEs</span></a>
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<a href="./ODEs/euler.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">49</span>&nbsp; <span class="chapter-title">Eulers method</span></a>
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<a href="./ODEs/solve.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">50</span>&nbsp; <span class="chapter-title">The problem-algorithm-solve interface</span></a>
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<a href="./ODEs/differential_equations.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">51</span>&nbsp; <span class="chapter-title">The <code>DifferentialEquations</code> suite</span></a>
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<a href="./differentiable_vector_calculus/vectors.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">53</span>&nbsp; <span class="chapter-title">Vectors and matrices</span></a>
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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>&nbsp; <span class="chapter-title">Vector-valued functions, <span class="math inline">\(f:R \rightarrow R^n\)</span></span></a>
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<a href="./differentiable_vector_calculus/scalar_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">55</span>&nbsp; <span class="chapter-title">Scalar functions</span></a>
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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>&nbsp; <span class="chapter-title">Applications with scalar functions</span></a>
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<a href="./differentiable_vector_calculus/vector_fields.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">57</span>&nbsp; <span class="chapter-title">Functions <span class="math inline">\(R^n \rightarrow R^m\)</span></span></a>
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<a href="./differentiable_vector_calculus/plots_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">58</span>&nbsp; <span class="chapter-title">2D and 3D plots in Julia with Plots</span></a>
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Hass, Joel R., Christopher E. Heil, and Maurice D. Weir. 2018.
<em>Thomas Calculus</em>. Pearson.
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Knill, Oliver. n.d. <span>“Some Teaching Notes.”</span> <a href="https://people.math.harvard.edu/~knill/teach/index.html">https://people.math.harvard.edu/~knill/teach/index.html</a>.
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Schey, H. M. 1997. <em>Div, Grad, Curl, and All That</em>. W.W. Norton.
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Strang, Gilbert. n.d. <span><span>MS Windows NT</span> Kernel
Description.”</span> <a href="https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/">https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/</a>.
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