diff --git a/course/index.html b/course/index.html index 08b0558..9d5ffe9 100755 --- a/course/index.html +++ b/course/index.html @@ -2,7 +2,7 @@ - + diff --git a/course/lunr-pretext-search-index.js b/course/lunr-pretext-search-index.js index 88fa1dd..1710b3b 100755 --- a/course/lunr-pretext-search-index.js +++ b/course/lunr-pretext-search-index.js @@ -16,7 +16,7 @@ var ptx_lunr_docs = [ "type": "Worksheet", "number": "", "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", @@ -60,8 +60,8 @@ var ptx_lunr_docs = [ "url": "recitation-calculus-review.html#thm-FTC", "type": "Theorem", "number": "1", - "title": "", - "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 . " + "title": "Fundamental Theorem of Calculus.", + "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", diff --git a/course/recitation-calculus-review-printable.html b/course/recitation-calculus-review-printable.html index 2153435..54a7483 100755 --- a/course/recitation-calculus-review-printable.html +++ b/course/recitation-calculus-review-printable.html @@ -228,20 +228,20 @@ eBookConfig.enable_chatcodes = false;
πŸ”—
πŸ”—

-Theorem 1. +Theorem 1. Fundamental Theorem of Calculus.

-
-
If \(F(x)\) is an antiderivative of \(f(x)\)β€”i.e., if \(F'(x) = f(x)\)β€”then the Fundamental Theorem of Calculus (FTC) says:
-
+
+
If \(F(x)\) is an antiderivative of \(f(x)\)β€”i.e., if \(F'(x) = f(x)\)β€”then:
+
\begin{gather*} \int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a). \end{gather*}
If \(f(x)\) is a probability density function (don’t worry about what that means for now), then integrals such as \(\int_a^b f(x)\ dx\) are used to calculate certain probabilities, and so are function values of the form \(F(x)\text{.}\)
-
πŸ”—
+
πŸ”—
-
πŸ”—

5.

+
πŸ”—

5.

Practice with the following integrals:
diff --git a/course/recitation-calculus-review.html b/course/recitation-calculus-review.html index ab9a2c9..582668c 100755 --- a/course/recitation-calculus-review.html +++ b/course/recitation-calculus-review.html @@ -213,20 +213,20 @@ eBookConfig.enable_chatcodes = false;
πŸ”—
πŸ”—

-Theorem 1. +Theorem 1. Fundamental Theorem of Calculus.

-
-
If \(F(x)\) is an antiderivative of \(f(x)\)β€”i.e., if \(F'(x) = f(x)\)β€”then the Fundamental Theorem of Calculus (FTC) says:
-
+
+
If \(F(x)\) is an antiderivative of \(f(x)\)β€”i.e., if \(F'(x) = f(x)\)β€”then:
+
\begin{gather*} \int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a). \end{gather*}
If \(f(x)\) is a probability density function (don’t worry about what that means for now), then integrals such as \(\int_a^b f(x)\ dx\) are used to calculate certain probabilities, and so are function values of the form \(F(x)\text{.}\)
-
πŸ”—
+
πŸ”—
-
πŸ”—

5.

+
πŸ”—

5.

Practice with the following integrals: