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182 lines
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HTML
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HTML
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<div style="float:right; width:150px; text-align:right;"> </div>
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<div style="margin:0 auto;">
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<h1 class="center">Calculus</h1>
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</div>
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</div>
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<div style="clear:both"></div>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/small-stones.jpg" alt="small stones" height="150" width="200"></p>
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<p class="center">The word Calculus comes from Latin meaning "small stone",<br>
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Because it is like understanding something by looking at small pieces.</p>
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<p><b>Differential Calculus</b> cuts something into small pieces to find how it changes. <b><br>
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</b></p>
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<p><b>Integral Calculus</b> joins (integrates) the small pieces together to find how much there is.</p>
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<p> </p>
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<div class="center80">
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/speedometer-0.jpg" alt="speedometer" height="102" width="150"></p>
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<p>Read <a href="introduction.html">Introduction to Calculus</a> or <i>"how fast <b>right now</b>?"</i></p>
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<div style="clear:both"></div>
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</div>
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<h2>Limits</h2>
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<p>Limits are all about approaching. Sometimes you can't work something out directly, but you <b>can</b> see what it should be as you get closer and closer!</p>
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<p><img src="../sets/images/function-reciprocal-pos.svg" alt="graph 1/x" height="163" width="266"></p>
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<ul class="large">
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<li><a href="limits.html">Introduction to Limits</a></li>
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<li><a href="limits-infinity.html">Limits and Infinity</a></li>
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<li><a href="limits-evaluating.html">Evaluating Limits</a></li>
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<li><a href="limits-formal.html">Limits (Formal Definition)</a></li>
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<li><a href="l-hopitals-rule.html">L'Hôpital's Rule</a></li>
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</ul>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/continuous-yes.svg" alt="continuous" height="103" width="191"></p>
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<p> </p>
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<ul class="large">
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<li><a href="continuity.html">Continuous Functions</a></li>
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</ul><div style="clear:both"></div>
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<h2>Derivatives (Differential Calculus)</h2>
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<p>The Derivative is the "rate of change" or slope of a function.</p>
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<p style="float:left; margin: 0 40px 5px 0;"><img src="images/slope-x2-2.svg" alt="slope x^2 at 2 has slope 4" height="206" width="165"></p>
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<ul class="large">
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<li><a href="derivatives-introduction.html">Introduction to Derivatives</a></li>
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<li><a href="slope-function-point.html">Slope of a Function at a Point (Interactive)</a></li>
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<li><a href="derivatives-dy-dx.html">Derivatives as dy/dx</a></li>
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<li><a href="derivative-plotter.html">Derivative Plotter (Interactive)</a></li>
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<li><a href="derivatives-rules.html">Derivative Rules</a></li>
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<li><a href="power-rule.html">Power Rule</a></li>
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<li><a href="product-rule.html">Product Rule</a></li>
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<li><a href="second-derivative.html">Second Derivative</a> and <a href="second-derivative-animation.html">Second Derivative Animation</a></li>
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<li><a href="derivatives-partial.html">Partial Derivatives</a></li>
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<li><a href="differentiable.html">Differentiable</a></li>
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<li><a href="maxima-minima.html">Finding Maxima and Minima using Derivatives</a></li>
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<li><a href="concave-up-down-convex.html">Concave Upwards and Downwards</a> and <a href="inflection-points.html">Inflection Points</a></li>
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<li><a href="implicit-differentiation.html">Implicit Differentiation</a></li>
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<li><a href="../algebra/taylor-series.html">Taylor Series</a> (uses derivatives)</li>
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<li>(Advanced) <a href="derivatives-trig-proof.html">Proof of the Derivatives of
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sin, cos and tan</a></li>
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</ul>
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<h2>Integration (Integral Calculus)</h2>
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<p>Integration can be used to find areas, volumes, central points and many useful things.</p>
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<span style="float:left; margin: 0 40px 5px 0;"><img src="images/integral-area.svg" alt="integral area = ?" height="179" width="217"></span>
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<ul class="large">
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<li><a href="integration-introduction.html">Introduction to Integration</a></li>
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<li><a href="derivative-vs-integral.html">Graphical Intro to Derivatives and Integrals</a></li>
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<li><a href="integration-rules.html">Integration Rules</a></li>
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<li><a href="integration-by-parts.html">Integration by Parts</a></li>
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<li><a href="integration-by-substitution.html">Integration by Substitution</a></li>
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<li><a href="integration-definite.html">Definite Integrals</a></li>
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<li><a href="arc-length.html">Arc Length</a></li>
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<li><a href="integral-approximations.html">Integral Approximations</a></li>
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<li><a href="integral-approximation-calculator.html">Integral Approximations Calculator and Graph</a></li>
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<li><a href="solids-revolution-disk-washer.html">Solids of Revolution by Disks and Washers</a></li>
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<li><a href="solids-revolution-shells.html">Solids of Revolution by Shells</a></li>
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<li><a href="fourier-series.html">Fourier Series</a> and <a href="fourier-series-graph.html">Fourier Series Grapher</a></li>
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</ul>
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<h2>Differential Equations</h2>
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<p>In our world things change, and <b>describing how they change</b> often ends up as a Differential Equation: an equation with a <b>function</b> and one or more of its <b>derivatives</b>:</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/diff-eq-1.svg" alt="differential equation y + dy/dx = 5x" height="123" width="188"></p>
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<ul class="large">
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<li><a href="differential-equations.html">Introduction to Differential Equations</a></li>
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<li><a href="differential-equations-solution-guide.html">Differential Equations Solution Guide</a></li>
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<li><a href="separation-variables.html">Separation of Variables</a></li>
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<li><a href="differential-equations-first-order-linear.html">First Order Linear Differential Equations </a></li>
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<li><a href="differential-equations-homogeneous.html">Homogeneous Differential Equations </a> (<a href="homogeneous-function.html">Homogeneous Functions</a>)</li>
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<li><a href="differential-equations-bernoulli.html">The Bernoulli Differential Equation</a></li>
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<li><a href="differential-equations-exact-factors.html">Exact Equations and Integrating Factors</a></li> </ul>
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<p>Second Order Differential Equations:</p>
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<ul class="large">
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<li><a href="differential-equations-second-order.html">Second Order Differential Equations</a></li>
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<li><a href="differential-equations-undetermined-coefficients.html">The Method of Undetermined Coefficients</a></li>
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<li><a href="differential-equations-variation-parameters.html">The Method of Variation of Parameters</a></li>
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</ul>
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<p> </p>
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<p>If you want more Calculus topics covered, <a href="../contact.html">let me know which ones</a>.</p>
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<h3>Bonus Topic</h3>
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<ul class="large">
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<li><a href="bifurcation.html">Bifurcation</a></li>
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</ul>
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