diff --git a/README.md b/README.md index c83971a..fed7720 100644 --- a/README.md +++ b/README.md @@ -62,7 +62,7 @@ MATLAB® is used throughout. Tools from the Symbolic Math Toolbox™ are used fr | [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)
$\displaystyle {\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$
                    $\displaystyle =(y^2 -2y+2)e^y +C$
| +| [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](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=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)
$\displaystyle {\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$
                    $\displaystyle =(y^2 -2y+2)e^y +C$
|