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Remove unnecessary line breaks from table
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eszmw committed Feb 16, 2024
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# Scripts
| **Full Script** <br> | **Visualizations** <br> | **Learning Goals** <br> In this script, students will... <br> | **Practice** <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="Family of antiderivatives"> <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="Animated family of antiderivatives"> <br> | - see a graphical presentation of the concept of general antiderivatives. <br> - 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="Distance traveled by skier"> <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="Signed area under a curve"> <br> | - explain the fundamental theorem of calculus. <br> - see why the Fundamental Theorem of Calculus makes sense graphically. <br> - 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="Better approximation with smaller rectangles"> <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="Approximation by rectangles"> <br> | - 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> | - explain and apply the trapezoidal approximation. <br> - explain why increasing the number of intervals in an approximation will decrease the error. <br> - 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="f(flower)"> <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="Animation of dx and du"> <br> | - explain what the method of substitution is and how it works. <br> - develop fluency with computing integrals of combinations of <br>powers, sines, cosines, exponentials and logarithms that are solvable <br>by substitution by hand. <br> - 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="Geometric integration by parts"> <br> | [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx) <br> <img src="Images/ibp-generated.png" width="135" alt="Integration horizontally and vertically"> <br> | - explain what the method of integration by parts is and how it works. <br> - develop fluency with computing integrals involving powers, sines,<br> cosines, exponentials and logarithms that are solvable by integration by <br>parts by hand. <br> - 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> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $\displaystyle =(y^2 -2y+2)e^y +C$ <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="Family of antiderivatives"> <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="Animated family of antiderivatives"> <br> | - see a graphical presentation of the concept of general antiderivatives. <br> - 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> $\displaystyle {\int \sin (3z)\;dz=-\frac{\cos (3z)}{3}+C}$ <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="Distance traveled by skier"> <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="Signed area under a curve"> <br> | - explain the fundamental theorem of calculus. <br> - see why the Fundamental Theorem of Calculus makes sense graphically. <br> - 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> $\displaystyle {\int_1^3 \frac{1}{w^2 }\;dw=-\frac{1}{3}+1=\frac{2}{3}}$ <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="Better approximation with smaller rectangles"> <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="Approximation by rectangles"> <br> | - 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> | - explain and apply the trapezoidal approximation. <br> - explain why increasing the number of intervals in an approximation will decrease the error. <br> - 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="f(flower)"> <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="Animation of dx and du"> <br> | - explain what the method of substitution is and how it works. <br> - develop fluency with computing integrals of combinations of powers, sines, cosines, exponentials and logarithms that are solvable <br>by substitution by hand. <br> - 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="Geometric integration by parts"> <br> | [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx) <br> <img src="Images/ibp-generated.png" width="135" alt="Integration horizontally and vertically"> <br> | - explain what the method of integration by parts is and how it works. <br> - develop fluency with computing integrals involving powers, sines, cosines, exponentials and logarithms that are solvable by integration by <br>parts by hand. <br> - 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> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $\displaystyle =(y^2 -2y+2)e^y +C$ <br> |

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