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@@ -16,10 +16,10 @@ This curriculum module contains interactive [MATLAB® live scripts](https://www. | |
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| ## Background | ||
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| You can use these live scripts as [demonstrations](#H_9AAE657C) in lectures, class [activities](#H_EB6194F8), or interactive [assignments](#H_175C7D50) outside of class. Calculus \- Integrals covers [Riemann sum](#H_1F9663E8) approximations to definite integrals, indefinite integrals as [antiderivatives](#H_BA1C166C), and the [fundamental theorem of calculus](#H_A543F16F). It also covers the indefinite integrals of powers, exponentials, natural logarithms, sines, and cosines as well as [substitution](#H_A0468BE8) and [integration by parts](#H_D389B1B1). Applications include area and power. In addition to the[full scripts](#H_EB6194F8), [visualizations](#H_9AAE657C), and [practice scripts](#H_175C7D50) there is a [Calculus Flashcards app](#H_1F9459BC) included as well. | ||
| You can use these live scripts as [demonstrations](#H_9AAE657C) in lectures, class activities, or interactive assignments outside of class. Calculus \- Integrals covers Riemann sum approximations to definite integrals, indefinite integrals as antiderivatives, and the fundamental theorem of calculus. It also covers the indefinite integrals of powers, exponentials, natural logarithms, sines, and cosines as well as substitution and integration by parts. Applications include area and power. In addition to the full scripts, visualizations, and practice scripts there is a [Calculus Flashcards app](#H_1F9459BC) included as well. | ||
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| The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the <img src="Images/EndIcon.png" width="19" alt="image_0.png"> Stop button in the **RUN** section of the **Live Editor** tab in the MATLAB Toolstrip. | ||
| The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the <img src="READMEtest_media/image_0.png" width="19" alt="image_0.png"> Stop button in the **RUN** section of the **Live Editor** tab in the MATLAB Toolstrip. | ||
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| Looking for more? Find an issue? Have a suggestion? Please contact the [MathWorks online teaching team](mailto:%[email protected]). | ||
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@@ -56,13 +56,13 @@ Ensure you have all the required products ([listed below](#H_E850B4FF)) installe | |
| MATLAB® is used throughout. Tools from the Symbolic Math Toolbox™ are used frequently as well. | ||
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| # Scripts | ||
| | **Topic** <br> | **Full Script** <br> | **Visualizations** <br> | **Learning Goals** <br> In this script, students will... <br> | **Practice** <br> | | ||
| [Apply the Fundamental Theorem of Calculus](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremPractice.mlx)| **Full Script** <br> | **Visualizations** <br> | **Learning Goals** <br> In this script, students will... <br> | **Practice** <br> | | ||
| | :-- | :-- | :-- | :-- | :-- | | ||
| | [Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Antiderivatives.mlx) <br> | [Antiderivatives.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Antiderivatives.mlx) <br> <img src="Images/adf.png" width="135" alt="image_3.png"> <br> | [Visualizing Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesViz.mlx) <br> <img src="Images/family.gif" width="135" alt="image_4.gif"> <br> | <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> see a graphical presentation of the concept of general antiderivatives. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> develop computational fluency with the antiderivatives of powers, sines, cosines, and exponentials. <br> | [Calculate Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesPractice.mlx) <br> [ <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;{\int | space;\sin | space;(3z)\;dz=-\frac{\cos | space;(3z)}{3}+C} | space;"> ](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesPractice.mlx) <br> | | ||
| | [Fundamental Theorem of Calculus](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx) <br> | [FundamentalTheorem.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx) <br> <img src="Images/Ski-Area.png" width="135" alt="image_5.png"> <br> | [Visualizing the FTC](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx) <br> <img src="Images/FTC-generated.png" width="135" alt="image_6.png"> <br> | <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> explain the fundamental theorem of calculus. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> see why the Fundamental Theorem of Calculus makes sense graphically. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> develop computational fluency for definite integrals involving linear and rational combinations of powers, sines, cosines, exponentials and natural logarithms. <br> | [Apply the Fundamental Theorem of Calculus](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremPractice.mlx) <br> [ <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;{\int_1^3 | space;\frac{1}{w^2 | space;}\;dw=-\frac{1}{3}+1=\frac{2}{3}} | space;"> ](./FundamentalTheoremPractice.mlx) <br> | | ||
| | [Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx) <br> | [Riemann.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx) <br> <img src="Images/animSolar.gif" width="135" alt="image_7.gif"> <br> | [Visualizing Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx) <br> <img src="Images/AreaUnderCurve.png" width="135" alt="image_8.png"> <br> | <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> explain and apply the different approximations computed by a left\-endpoint, right\-endpoint, midpoint, maximum, or minimum method of selecting a height value in a Riemann sum. <br> | <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> explain and apply the trapezoidal approximation. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> explain why increasing the number of intervals in an approximation will decrease the error. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> discuss the implications for applying calculus in applications with values that are discrete or continuous. <br> | | ||
| | [Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx) <br> | [Substitution.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx) <br> <img src="Images/SubstIm.png" width="135" alt="image_9.png"> <br> | [Visualizing Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx) <br> <img src="Images/animSubst.gif" width="135" alt="image_10.gif"> <br> | <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> explain what the method of substitution is and how it works. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> develop fluency with computing integrals of combinations of powers, sines, cosines, exponentials and logarithms that are solvable by substitution by hand. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> see a graphical understanding of the method of substitution. <br> | [Apply the method of substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionPractice.mlx) <br> [ <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;{\int | space;\frac{\cos | space;\left(\ln | space;(t)+1\right)}{t}\;dt=\sin | space;\left(\ln | space;(t)+1\right)+C} | space;"> ](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionPractice.mlx) <br> | | ||
| | [Integration by Parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx) <br> | [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx) <br> <img src="Images/IBP.png" width="135" alt="image_11.png"> <br> | [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx) <br> <img src="Images/ibp-generated.png" width="135" alt="image_12.png"> <br> | <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> explain what the method of integration by parts is and how it works. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> develop fluency with computing integrals involving powers, sines, cosines, exponentials and logarithms that are solvable by integration by parts by hand. <br> <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;\bullet | space;"> see a graphical understanding of the integration by parts formula. <br> | [Apply the method of integration by parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsPractice.mlx) <br> [ <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;{\int | space;y^2 | space;e^y | space;\;dy=y^2 | space;e^y | space;-2ye^y | space;+2e^y | space;+C} | space;"> ](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsPractice.mlx) <br> [ <img src="https://latex.codecogs.com/svg.latex?\inline | space; | space;=(y^2 | space;-2y+2)e^y | space;+C | space;"> ](matlab: edit practiceByParts.mlx) <br> | | ||
| | [Antiderivatives.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Antiderivatives.mlx) <br> <img src="Images/adf.png" width="135" alt="image_3.png"> <br> | [Visualizing Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesViz.mlx) <br> <img src="Images/family.gif" width="135" alt="image_4.gif"> <br> | $\bullet$ see a graphical presentation of the concept of general antiderivatives. <br> $\bullet$ develop computational fluency with the antiderivatives of powers, <br> sines, cosines, and exponentials. <br> | [Calculate Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesPractice.mlx) <br> $\displaystyle {\int \sin (3z)\;dz=-\frac{\cos (3z)}{3}+C}$ <br> | | ||
| | [FundamentalTheorem.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx) <br> <img src="Images/Ski-Area.png" width="135" alt="image_5.png"> <br> | [Visualizing the FTC](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx) <br> <img src="Images/FTC-generated.png" width="135" alt="image_6.png"> <br> | $\bullet$ explain the fundamental theorem of calculus. <br> $\bullet$ see why the Fundamental Theorem of Calculus makes sense graphically. <br> $\bullet$ develop computational fluency for definite integrals involving linear and <br>rational combinations of powers, sines, cosines, exponentials and natural <br>logarithms. <br> | [Apply the Fundamental Theorem of Calculus](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremPractice.mlx) <br> $\displaystyle {\int_1^3 \frac{1}{w^2 }\;dw=-\frac{1}{3}+1=\frac{2}{3}}$ <br> | | ||
| | [Riemann.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx) <br> <img src="Images/animSolar.gif" width="135" alt="image_7.gif"> <br> | [Visualizing Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx) <br> <img src="Images/AreaUnderCurve.png" width="135" alt="image_8.png"> <br> | $\bullet$ explain and apply the different approximations computed by a <br>left\-endpoint, right\-endpoint, midpoint, maximum, or minimum <br>method of selecting a height value in a Riemann sum. <br> | $\bullet$ explain and apply the trapezoidal approximation. <br> $\bullet$ explain why increasing the number of intervals in an approximation will decrease the error. <br> $\bullet$ discuss the implications for applying calculus in applications with values that are discrete or continuous. <br> | | ||
| | [Substitution.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx) <br> <img src="Images/SubstIm.png" width="135" alt="image_9.png"> <br> | [Visualizing Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx) <br> <img src="Images/animSubst.gif" width="135" alt="image_10.gif"> <br> | $\bullet$ explain what the method of substitution is and how it works. <br> $\bullet$ develop fluency with computing integrals of combinations of <br>powers, sines, cosines, exponentials and logarithms that are solvable <br>by substitution by hand. <br> $\bullet$ see a graphical understanding of the method of substitution. <br> | [Apply the method of substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionPractice.mlx) <br> $\displaystyle {\int \frac{\cos \left(\ln (t)+1\right)}{t}\;dt=\sin \left(\ln (t)+1\right)+C}$ <br> | | ||
| | [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx) <br> <img src="Images/IBP.png" width="135" alt="image_11.png"> <br> | [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx) <br> <img src="Images/ibp-generated.png" width="135" alt="image_12.png"> <br> | $\bullet$ explain what the method of integration by parts is and how it works. <br> $\bullet$ develop fluency with computing integrals involving powers, sines,<br> cosines, exponentials and logarithms that are solvable by integration by <br>parts by hand. <br> $\bullet$ see a graphical understanding of the integration by parts formula. <br> | [Apply the method of integration by parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsPractice.mlx) <br> $\displaystyle {\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$ <br> $\displaystyle =(y^2 -2y+2)e^y +C$ <br> | | ||
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