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Edit equations to display properly
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eszmw authored Oct 21, 2024
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Expand Up @@ -60,7 +60,7 @@ MATLAB® is used throughout. Tools from the Symbolic Math Toolbox™ are used fr
| [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="Ski-Area.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx) <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="FTC-generated.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx) <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 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 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="animSolar.gif">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx) <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="AreaUnderCurve.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx) <br> | $\bullet$ 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> | $\bullet$ 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](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="SubstIm.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="animSubst.gif">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx) <br> | $\bullet$ explain what the method of substitution is and how it works. <br> $\bullet$ develop fluency with computing integrals of combinations of powers, sines, cosines, exponentials and logarithms that are solvable 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> |
| [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="IBP.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx) <br> | [Visualizing Integration by Parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx) <br> [<img src="Images/ibp-generated.png" width="135" alt="ibp-generated.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx) <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, cosines, exponentials and logarithms that are solvable by integration by 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> [ ${\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$ ](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=cripts/ByPartsPractice.mlx) <br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [ $=(y^2 -2y+2)e^y +C$ ](matlab: edit practiceByParts.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="IBP.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx) <br> | [Visualizing Integration by Parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx) <br> [<img src="Images/ibp-generated.png" width="135" alt="ibp-generated.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx) <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, cosines, exponentials and logarithms that are solvable by integration by 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> $\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C$ <br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $=(y^2 -2y+2)e^y +C$ <br> |
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# [Calculus Flashcards App](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Apps/CalculusFlashcards.mlapp&focus=true)
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