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||**In this script, students will...**|**Applications**|
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| <imgsrc="Images/drawnSolutionV2.png"width="171"alt="drawnSolutionV2.png"> |<br>- classify ODEs as autonomous or non-autonomous <br>- describe how a slope field is generated <br>- draw ODE solutions through the slope field by hand <br>- explain the physical meaning of terms in an energy balance climate model <br>- plot solutions of the energy balance climate model | Energy balance model<imgsrc="Images/radiation_reflection.png"width="171"alt="radiation_reflection.png"> |
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| <imgsrc="Images/drawnSolutionV2.png"width="250"alt="drawnSolutionV2.png"> |<br>- classify ODEs as autonomous or non-autonomous <br>- describe how a slope field is generated <br>- draw ODE solutions through the slope field by hand <br>- explain the physical meaning of terms in an energy balance climate model <br>- plot solutions of the energy balance climate model | Energy balance model<imgsrc="Images/radiation_reflection.png"width="171"alt="radiation_reflection.png"> |
||**In this script, students will...**| Application |
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| <imgsrc="Images/EBMSlopeField.png"width="171"alt="EBMSlopeField.png"> |<br>- solve for equilibria of autonomous first order ODEs <br>- classify equilibria as stable, unstable, or semi-stable <br>- draw phase line portraits of autonomous ODEs and relate them to the slope field <br>- find the equilibria of the energy balance climate model <br>- describe the real-world meaning of the climate model equilibria | Energy balance model<imgsrc="Images/radiationV2.png"width="171"alt="radiationV2.png"> |
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| <imgsrc="Images/EBMSlopeField.png"width="250"alt="EBMSlopeField.png"> |<br>- solve for equilibria of autonomous first order ODEs <br>- classify equilibria as stable, unstable, or semi-stable <br>- draw phase line portraits of autonomous ODEs and relate them to the slope field <br>- find the equilibria of the energy balance climate model <br>- describe the real-world meaning of the climate model equilibria | Energy balance model<imgsrc="Images/radiationV2.png"width="171"alt="radiationV2.png"> |
||**In this script, students will...**| Application |
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| <imgsrc="Images/pp1.png"width="171"alt="pp1.png"> |<br>- write a second order ODE as a first order ODE system <br>- describe how a phase plane is generated <br>- relate solutions plotted on the phase plane to time series solution plots <br>- compare behaviors of the mass-spring-damper model under variations in the damping coefficient | <imgsrc="Images/pendulum3.jpeg"width="117"alt="pendulum3.jpeg"> |
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| <imgsrc="Images/pp1.png"width="220"alt="pp1.png"> |<br>- write a second order ODE as a first order ODE system <br>- describe how a phase plane is generated <br>- relate solutions plotted on the phase plane to time series solution plots <br>- compare behaviors of the mass-spring-damper model under variations in the damping coefficient | <imgsrc="Images/pendulum3.jpeg"width="117"alt="pendulum3.jpeg"> |
||**In this script, students will...**| Application |
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| <imgsrc="Images/ClassifyingSpiralsCenters.png"width="171"alt="ClassifyingSpiralsCenters.png"> |<br>- find equilibria of a second order ODE system <br>- compute the eigenvalues of the coefficient matrix of a linear ODE system <br>- classify equilibria as nodes, saddles, spirals, or centers <br>- categorize the behavior of the mass-spring-damper model by analyzing its coefficient matrix | <imgsrc="Images/mass_spring_damper.jpeg"width="165"alt="mass_spring_damper.jpeg"> |
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| <imgsrc="Images/ClassifyingSpiralsCenters.png"width="220"alt="ClassifyingSpiralsCenters.png"> |<br>- find equilibria of a second order ODE system <br>- compute the eigenvalues of the coefficient matrix of a linear ODE system <br>- classify equilibria as nodes, saddles, spirals, or centers <br>- categorize the behavior of the mass-spring-damper model by analyzing its coefficient matrix | <imgsrc="Images/mass_spring_damper.jpeg"width="165"alt="mass_spring_damper.jpeg"> |
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# Related Courseware Modules
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## [Phase Plane and Slope Field](https://www.mathworks.com/matlabcentral/fileexchange/91705-phase-plane-and-slope-field-apps)
Or feel free to explore our other [modular courseware content](https://www.mathworks.com/matlabcentral/fileexchange/?q=tag%3A%22courseware+module%22&sort=downloads_desc_30d).
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