From f139e8f741767ce7b058075c85fb1ad66d4761ad Mon Sep 17 00:00:00 2001 From: Emma Smith Zbarsky <88841524+eszmw@users.noreply.github.com> Date: Thu, 15 Feb 2024 21:33:09 -0500 Subject: [PATCH] Update README.md Remove unnecessary line breaks from table --- README.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/README.md b/README.md index f5fcd72..c83971a 100644 --- a/README.md +++ b/README.md @@ -58,11 +58,11 @@ MATLAB® is used throughout. Tools from the Symbolic Math Toolbox™ are used fr # Scripts | **Full Script**
| **Visualizations**
| **Learning Goals**
In this script, students will...
| **Practice**
| | :-- | :-- | :-- | :-- | - | [Antiderivatives.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Antiderivatives.mlx)
Family of antiderivatives
| [Visualizing Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesViz.mlx)
Animated family of antiderivatives
| - see a graphical presentation of the concept of general antiderivatives.
- develop computational fluency with the antiderivatives of powers,
sines, cosines, and exponentials.
| [Calculate Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesPractice.mlx)
$\displaystyle {\int \sin (3z)\;dz=-\frac{\cos (3z)}{3}+C}$
| -| [FundamentalTheorem.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx)
Distance traveled by skier
| [Visualizing the FTC](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx)
Signed area under a curve
| - explain the fundamental theorem of calculus.
- see why the Fundamental Theorem of Calculus makes sense graphically.
- 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.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx)
Better approximation with smaller rectangles
| [Visualizing Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx)
Approximation by rectangles
| - 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.
| - explain and apply the trapezoidal approximation.
- explain why increasing the number of intervals in an approximation will decrease the error.
- discuss the implications for applying calculus in applications with values that are discrete or continuous.
| -| [Substitution.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx)
f(flower)
| [Visualizing Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx)
Animation of dx and du
| - explain what the method of substitution is and how it works.
- develop fluency with computing integrals of combinations of
powers, sines, cosines, exponentials and logarithms that are solvable
by substitution by hand.
- 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)
$\displaystyle {\int \frac{\cos \left(\ln (t)+1\right)}{t}\;dt=\sin \left(\ln (t)+1\right)+C}$
| -| [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
Geometric integration by parts
| [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx)
Integration horizontally and vertically
| - explain what the method of integration by parts is and how it works.
- develop fluency with computing integrals involving powers, sines,
cosines, exponentials and logarithms that are solvable by integration by
parts by hand.
- 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)
$\displaystyle {\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$
                    $\displaystyle =(y^2 -2y+2)e^y +C$
| + | [Antiderivatives.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Antiderivatives.mlx)
Family of antiderivatives
| [Visualizing Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesViz.mlx)
Animated family of antiderivatives
| - see a graphical presentation of the concept of general antiderivatives.
- develop computational fluency with the antiderivatives of powers, sines, cosines, and exponentials.
| [Calculate Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesPractice.mlx)
$\displaystyle {\int \sin (3z)\;dz=-\frac{\cos (3z)}{3}+C}$
| +| [FundamentalTheorem.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx)
Distance traveled by skier
| [Visualizing the FTC](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx)
Signed area under a curve
| - explain the fundamental theorem of calculus.
- see why the Fundamental Theorem of Calculus makes sense graphically.
- 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.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx)
Better approximation with smaller rectangles
| [Visualizing Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx)
Approximation by rectangles
| - 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.
| - explain and apply the trapezoidal approximation.
- explain why increasing the number of intervals in an approximation will decrease the error.
- discuss the implications for applying calculus in applications with values that are discrete or continuous.
| +| [Substitution.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx)
f(flower)
| [Visualizing Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx)
Animation of dx and du
| - explain what the method of substitution is and how it works.
- develop fluency with computing integrals of combinations of powers, sines, cosines, exponentials and logarithms that are solvable
by substitution by hand.
- 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)
$\displaystyle {\int \frac{\cos \left(\ln (t)+1\right)}{t}\;dt=\sin \left(\ln (t)+1\right)+C}$
| +| [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx)
Geometric integration by parts
| [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx)
Integration horizontally and vertically
| - explain what the method of integration by parts is and how it works.
- develop fluency with computing integrals involving powers, sines, cosines, exponentials and logarithms that are solvable by integration by
parts by hand.
- 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)
$\displaystyle {\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$
                    $\displaystyle =(y^2 -2y+2)e^y +C$
|