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course/index.html
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<html> <html>
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course/lunr-pretext-search-index.js
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@@ -16,7 +16,7 @@ var ptx_lunr_docs = [
"type": "Worksheet", "type": "Worksheet",
"number": "", "number": "",
"title": "Calculus Review", "title": "Calculus Review",
"body": " Calculus Review In Calculus I, you learned about derivatives, antiderivatives, and definite integrals. All of these will make an appearance in the context of probability density functions, cumulative distribution functions, and probability calculations in continuous sample spaces, so it will be useful to refresh your memory and practice some calculations. The Power Rule for derivatives states: The Power Rule for antiderivatives states: Practice with the following derivatives: Practice with the following antiderivatives: If is an antiderivative of i.e., if then the Fundamental Theorem of Calculus (FTC) says: If is a probability density function (don't worry about what that means for now), then integrals such as are used to calculate certain probabilities, and so are function values of the form . Practice with the following integrals: " "body": " Calculus Review In Calculus I, you learned about derivatives, antiderivatives, and definite integrals. All of these will make an appearance in the context of probability density functions, cumulative distribution functions, and probability calculations in continuous sample spaces, so it will be useful to refresh your memory and practice some calculations. The Power Rule for derivatives states: The Power Rule for antiderivatives states: Practice with the following derivatives: Practice with the following antiderivatives: Fundamental Theorem of Calculus If is an antiderivative of i.e., if then: If is a probability density function (don't worry about what that means for now), then integrals such as are used to calculate certain probabilities, and so are function values of the form . Practice with the following integrals: "
}, },
{ {
"id": "recitation-calculus-review-3", "id": "recitation-calculus-review-3",
@@ -60,8 +60,8 @@ var ptx_lunr_docs = [
"url": "recitation-calculus-review.html#thm-FTC", "url": "recitation-calculus-review.html#thm-FTC",
"type": "Theorem", "type": "Theorem",
"number": "1", "number": "1",
"title": "", "title": "Fundamental Theorem of Calculus.",
"body": " If is an antiderivative of i.e., if then the Fundamental Theorem of Calculus (FTC) says: If is a probability density function (don't worry about what that means for now), then integrals such as are used to calculate certain probabilities, and so are function values of the form . " "body": " Fundamental Theorem of Calculus If is an antiderivative of i.e., if then: If is a probability density function (don't worry about what that means for now), then integrals such as are used to calculate certain probabilities, and so are function values of the form . "
}, },
{ {
"id": "recitation-calculus-review-8", "id": "recitation-calculus-review-8",
course/recitation-calculus-review-printable.html
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@@ -228,20 +228,20 @@ eBookConfig.enable_chatcodes = false;
<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="autopermalink" data-description="Worksheet Exercise 4"><a href="#recitation-calculus-review-6" title="Copy heading and permalink for Worksheet Exercise 4" aria-label="Copy heading and permalink for Worksheet Exercise 4">🔗</a></div></article><article class="theorem theorem-like" id="thm-FTC"><h3 class="heading"> <div class="autopermalink" data-description="Worksheet Exercise 4"><a href="#recitation-calculus-review-6" title="Copy heading and permalink for Worksheet Exercise 4" aria-label="Copy heading and permalink for Worksheet Exercise 4">🔗</a></div></article><article class="theorem theorem-like" id="thm-FTC"><h3 class="heading">
<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span> <span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Fundamental Theorem of Calculus.</span>
</h3> </h3>
<div class="para logical" id="thm-FTC-1-1"> <div class="para logical" id="thm-FTC-2-1">
<div class="para">If <span class="process-math">\(F(x)\)</span> is an antiderivative of <span class="process-math">\(f(x)\)</span>—i.e., if <span class="process-math">\(F'(x) = f(x)\)</span>—then the Fundamental Theorem of Calculus (FTC) says:</div> <div class="para">If <span class="process-math">\(F(x)\)</span> is an antiderivative of <span class="process-math">\(f(x)\)</span>—i.e., if <span class="process-math">\(F'(x) = f(x)\)</span>—then:</div>
<div class="displaymath process-math" id="thm-FTC-1-1-6"> <div class="displaymath process-math" id="thm-FTC-2-1-6">
\begin{gather*} \begin{gather*}
\int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a). \int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a).
\end{gather*} \end{gather*}
</div> </div>
<div class="para">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, and so are function values of the form <span class="process-math">\(F(x)\text{.}\)</span> <div class="para">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, and so are function values of the form <span class="process-math">\(F(x)\text{.}\)</span>
</div> </div>
<div class="autopermalink" data-description="Paragraph"><a href="#thm-FTC-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="autopermalink" data-description="Paragraph"><a href="#thm-FTC-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="autopermalink" data-description="Theorem 1"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 1" aria-label="Copy heading and permalink for Theorem 1">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-8"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3> <div class="autopermalink" data-description="Theorem 1: Fundamental Theorem of Calculus"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 1: Fundamental Theorem of Calculus" aria-label="Copy heading and permalink for Theorem 1: Fundamental Theorem of Calculus">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-8"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
<div class="para logical" id="recitation-calculus-review-8-1-1"> <div class="para logical" id="recitation-calculus-review-8-1-1">
<div class="para">Practice with the following integrals:</div> <div class="para">Practice with the following integrals:</div>
<div class="displaymath process-math" id="recitation-calculus-review-8-1-1-1"> <div class="displaymath process-math" id="recitation-calculus-review-8-1-1-1">
course/recitation-calculus-review.html
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@@ -213,20 +213,20 @@ eBookConfig.enable_chatcodes = false;
<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="autopermalink" data-description="Worksheet Exercise 4"><a href="#recitation-calculus-review-6" title="Copy heading and permalink for Worksheet Exercise 4" aria-label="Copy heading and permalink for Worksheet Exercise 4">🔗</a></div></article><article class="theorem theorem-like" id="thm-FTC"><h3 class="heading"> <div class="autopermalink" data-description="Worksheet Exercise 4"><a href="#recitation-calculus-review-6" title="Copy heading and permalink for Worksheet Exercise 4" aria-label="Copy heading and permalink for Worksheet Exercise 4">🔗</a></div></article><article class="theorem theorem-like" id="thm-FTC"><h3 class="heading">
<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span> <span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Fundamental Theorem of Calculus.</span>
</h3> </h3>
<div class="para logical" id="thm-FTC-1-1"> <div class="para logical" id="thm-FTC-2-1">
<div class="para">If <span class="process-math">\(F(x)\)</span> is an antiderivative of <span class="process-math">\(f(x)\)</span>—i.e., if <span class="process-math">\(F'(x) = f(x)\)</span>—then the Fundamental Theorem of Calculus (FTC) says:</div> <div class="para">If <span class="process-math">\(F(x)\)</span> is an antiderivative of <span class="process-math">\(f(x)\)</span>—i.e., if <span class="process-math">\(F'(x) = f(x)\)</span>—then:</div>
<div class="displaymath process-math" id="thm-FTC-1-1-6"> <div class="displaymath process-math" id="thm-FTC-2-1-6">
\begin{gather*} \begin{gather*}
\int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a). \int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a).
\end{gather*} \end{gather*}
</div> </div>
<div class="para">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, and so are function values of the form <span class="process-math">\(F(x)\text{.}\)</span> <div class="para">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, and so are function values of the form <span class="process-math">\(F(x)\text{.}\)</span>
</div> </div>
<div class="autopermalink" data-description="Paragraph"><a href="#thm-FTC-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="autopermalink" data-description="Paragraph"><a href="#thm-FTC-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="autopermalink" data-description="Theorem 1"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 1" aria-label="Copy heading and permalink for Theorem 1">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-8"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3> <div class="autopermalink" data-description="Theorem 1: Fundamental Theorem of Calculus"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 1: Fundamental Theorem of Calculus" aria-label="Copy heading and permalink for Theorem 1: Fundamental Theorem of Calculus">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-8"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
<div class="para logical" id="recitation-calculus-review-8-1-1"> <div class="para logical" id="recitation-calculus-review-8-1-1">
<div class="para">Practice with the following integrals:</div> <div class="para">Practice with the following integrals:</div>
<div class="displaymath process-math" id="recitation-calculus-review-8-1-1-1"> <div class="displaymath process-math" id="recitation-calculus-review-8-1-1-1">