diff --git a/README.md b/README.md index 3a9e458..82ab526 100644 --- a/README.md +++ b/README.md @@ -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)
| [FundamentalTheorem.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx)
[Ski-Area.png](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx)
| [Visualizing the FTC](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx)
[FTC-generated.png](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx)
| $\bullet$ explain the fundamental theorem of calculus.
$\bullet$ see why the Fundamental Theorem of Calculus makes sense graphically.
$\bullet$ develop computational fluency for definite integrals involving linear and rational combinations of powers, sines, cosines, exponentials and natural logarithms.
| [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)
$\displaystyle {\int_1^3 \frac{1}{w^2 }\;dw=-\frac{1}{3}+1=\frac{2}{3}}$
| | [Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx)
| [Riemann.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx)
[animSolar.gif](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx)
| [Visualizing Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx)
[AreaUnderCurve.png](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx)
| $\bullet$ 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.
| $\bullet$ explain and apply the trapezoidal approximation.
$\bullet$ explain why increasing the number of intervals in an approximation will decrease the error.
$\bullet$ discuss the implications for applying calculus in applications with values that are discrete or continuous.
| | [Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx)
| [Substitution.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx)
SubstIm.png
| [Visualizing Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx)
[animSubst.gif](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx)
| $\bullet$ explain what the method of substitution is and how it works.
$\bullet$ develop fluency with computing integrals of combinations of powers, sines, cosines, exponentials and logarithms that are solvable by substitution by hand.
$\bullet$ see a graphical understanding of the method of substitution.
| [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)
$\displaystyle {\int \frac{\cos \left(\ln (t)+1\right)}{t}\;dt=\sin \left(\ln (t)+1\right)+C}$
| -| [Integration by Parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
| [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
[IBP.png](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
| [Visualizing Integration by Parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx)
[ibp-generated.png](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx)
| $\bullet$ explain what the method of integration by parts is and how it works.
$\bullet$ develop fluency with computing integrals involving powers, sines, cosines, exponentials and logarithms that are solvable by integration by parts by hand.
$\bullet$ see a graphical understanding of the integration by parts formula.
| [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)
[ ${\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$ ](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=cripts/ByPartsPractice.mlx)
                   [ $=(y^2 -2y+2)e^y +C$ ](matlab: edit practiceByParts.mlx)
| +| [Integration by Parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
| [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
[IBP.png](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
| [Visualizing Integration by Parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx)
[ibp-generated.png](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsViz.mlx)
| $\bullet$ explain what the method of integration by parts is and how it works.
$\bullet$ develop fluency with computing integrals involving powers, sines, cosines, exponentials and logarithms that are solvable by integration by parts by hand.
$\bullet$ see a graphical understanding of the integration by parts formula.
| [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)
$\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C$
                   $=(y^2 -2y+2)e^y +C$
| | | | | | | # [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)