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Update with CharacteristicEquations and UndeterminedCoefficients
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README.md

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| <img src="Images/ChemicalConcentration.png" width="201" alt="ChemicalConcentration.png"> <br> | **In this script, students will...** <br> $\bullet$ find integrating factors of linear, first\-order ordinary differential equations <br> $\bullet$ solve equations analytically by multiplying by integrating factors <br> | **Applications** <br> $\bullet$ Chemical concentration <br> **Academic disciplines** <br> $\bullet$ Mathematics <br> $\bullet$ Chemistry <br> |
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## **CharacteristicEquations.mlx** **(Planned)**
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## [**CharacteristicEquations.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-ODEs&project=AppliedODEs.prj&file=Scripts/CharacteristicEquations.mlx)
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| <img src="Images/Circuit.png" width="201" alt="Circuit.png"> <br> | **In this script, students will...** <br> $\bullet$ find characteristic equations of linear, second\-order ordinary differential equations <br> $\bullet$ use the roots of characteristic equations to solve homogeneous equations analytically <br> | **Applications** <br> $\bullet$ RLC Circuits <br> $\bullet$ Mass\-spring\-damper <br> **Academic disciplines** <br> $\bullet$ Mathematics <br> $\bullet$ Engineering <br> $\bullet$ Physics <br> |
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## **UndeterminedCoefficients.mlx** **(Planned)**
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## [**UndeterminedCoefficients.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-ODEs&project=AppliedODEs.prj&file=Scripts/UndeterminedCoefficients.mlx)
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| <img src="Images/ChemicalBonds.png" width="202" alt="ChemicalBonds.png"> <br> | **In this script, students will...** <br> $\bullet$ solve linear, second\-order, nonhomogeneous ordinary differential equations analytically using the method of undetermined coefficients <br> | **Applications** <br> $\bullet$ Pendulum motion <br> $\bullet$ Chemical bonds <br> **Academic disciplines** <br> $\bullet$ Mathematics <br> $\bullet$ Physics <br> $\bullet$ Chemistry <br> |
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## **SystemsOfODEs.mlx** **(Planned)**
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## [**SystemsOfODEs.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-ODEs&project=AppliedODEs.prj&file=Scripts/SystemsOfODEs.mlx)
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| <img src="Images/Earthquake.png" width="201" alt="Earthquake.png"> <br> | **In this script, students will...** <br> $\bullet$ write systems of linear, homogeneous, first\-order differential equations in matrix form <br> $\bullet$ find eigenvalues and eigenvectors of these matrices <br> $\bullet$ solve systems of ODEs analytically using these eigenvalues and eigenvectors <br> | **Applications** <br> $\bullet$ SIR model of epidemiology <br> $\bullet$ Earthquake effects on buildings <br> **Academic disciplines** <br> $\bullet$ Mathematics <br> $\bullet$ Biology <br> $\bullet$ Engineering <br> |

README.mlx

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