Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations


Differential Equations

by Allen Wolmer

Mooculus Calculus Textbook Section 11.2 pp 193-195

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Slope fields

by Allen Wolmer

It may be hard or even impossible to find an explicit solution to for some differential equations. Fortunately, if the DE is 1st order we can graph the differential equation’s slope field and see the solution curves, even if we cannot write down their exact equation.

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Slope Fields

by Allen Wolmer

A Firefly Lectures video on this topic.

Video duration:   9:34

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Slope Field: Example 1

by Allen Wolmer

A Firefly Lectures video on this topic.

Video duration:  9:56

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ODE | Slope fields

by Allen Wolmer

A Youtube video on this topic.

Video duration:  4:39

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A Math League of America video on this topic.

Video duration:  18:53

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Slope Fields

by Allen Wolmer

A calculus applet illustrating the topic. Requires security enabled Java.

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Mooculus Calculus Textbook Exercises, Sect 11.2 p 196 (ex 9&10) (Ans p 253)

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 4 Model with mathematics.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

Slope Fields Exercises

by Allen Wolmer

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 4 Model with mathematics.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 4 Model with mathematics.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

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