https://arshadhs.github.io/tags/derivatives/Recent content in Derivatives on Arshad SiddiquiHugoen-ushttps://arshadhs.github.io/docs/ai/maths/020-calculus/Mon, 01 Jan 0001 00:00:00 +0000https://arshadhs.github.io/docs/ai/maths/020-calculus/<h1 id="calculus"> Calculus <a class="anchor" href="#calculus">#</a> </h1> <p>Calculus is:</p> <ul> <li>the mathematical framework for understanding and controlling how quantities change</li> <li>the mathematics of <strong>change</strong> and <strong>accumulation</strong></li> </ul> <p>It helps answer:</p> <ul> <li>How fast is something changing <strong>right now</strong>?</li> <li>What happens when inputs change <strong>slightly</strong>?</li> <li>Where is something <strong>maximum or minimum</strong>?</li> </ul> <p>It answers two big questions:</p> <ul> <li><strong>How fast is something changing right now?</strong> → derivatives (differentiation)</li> <li><strong>How much has accumulated over an interval?</strong> → integrals (integration)</li> </ul> <hr> <script src="https://arshadhs.github.io/mermaid.min.js"></script> <script>mermaid.initialize({ "flowchart": { "useMaxWidth":true }, "theme": "default" } )</script> <pre class="mermaid"> flowchart TD A[Calculus] --&gt; B[Limits] B --&gt; C[Continuity] B --&gt; D[Derivatives] B --&gt; E[Integrals] D --&gt; F[Optimisation: maxima/minima] D --&gt; G[ML: gradients &amp; learning] E --&gt; H[Accumulation: area/total change] </pre> <hr> <ul> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/">Vector Calculus</a> <ul> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/010-univariate-differentiation/">Differentiation of Univariate Functions</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/020-partial-derivatives-and-gradients/">Partial Differentiation and Gradients</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/030-vector-and-matrix-gradients/">Gradients of Vector-Valued and Matrix Functions</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/050-gradient-identities/">Useful Gradient Identities</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/060-backpropagation/">Backpropagation and Automatic Differentiation</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/070-higher-order-derivatives/">Higher-order derivatives</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/080-taylors-series/">Taylor’s series</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/04-vector-calculus/090-maxima-and-minima/">Maxima and Minima</a> </li> </ul> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/05-optimisation/">Continuous Optimisation</a> <ul> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/05-optimisation/gradient-descent/">Optimisation using Gradient Descent</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/05-optimisation/constrained-optimisation/">Constrained Optimisation</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/05-optimisation/lagrange-multipliers/">Lagrange Multipliers</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/05-optimisation/convex-optimisation/">Convex Optimisation</a> </li> </ul> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/06-nonlinear-optimisation/">Nonlinear Optimisation</a> <ul> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/06-nonlinear-optimisation/optimisation-challenges/">Challenges in Gradient-Based Optimisation</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/06-nonlinear-optimisation/stochastic-gradient-descent/">Stochastic Gradient Descent (SGD)</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/06-nonlinear-optimisation/momentum-methods/">Momentum-Based Learning</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/06-nonlinear-optimisation/adaptive-methods/">Adaptive Methods: AdaGrad, RMSProp, Adam</a> </li> <li> <a href="https://arshadhs.github.io/docs/ai/maths/020-calculus/06-nonlinear-optimisation/hyperparameter-tuning/">Tuning Hyperparameters and Preprocessing</a> </li> </ul> </li> </ul> <hr> <div class="book-steps "> <ol> <li> <h2 id="differential-calculus-rates-of-change"> Differential Calculus (Rates of Change) <a class="anchor" href="#differential-calculus-rates-of-change">#</a> </h2> <p>Studies <strong>how things change</strong>.</p>