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Mathematics · Grade 11

Differential Equations and Models

Learners read equations about rates of change as models. They verify solutions, sketch and interpret slope fields, approximate solutions with Euler's method, solve separable equations with initial conditions, and model exponential growth and decay, Newton's law of cooling and logistic growth, including equilibrium and long-run behavior.

  • 4 lessons
  • About 150 minutes
  • Differential equations check: 12 questions
  • Ways to answer: choose an answer, match pairs, type a number, put in order, true or false and write a short answer
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What learners will discover

  • Interpret differential equations as statements about rates and verify proposed solutions.
  • Interpret slope fields and approximate solutions with Euler's method.
  • Solve separable differential equations and initial value problems.
  • Model with exponential, cooling and logistic differential equations and interpret equilibria and long-run behavior.

Lessons

  1. Equations about rates 5 steps3 practiceabout 30 min
  2. Slope fields and Euler's method 5 steps3 practiceabout 36 min
  3. Separable equations 5 steps3 practiceabout 36 min
  4. Three classic models 6 steps3 practiceabout 48 min
  5. Differential equations check 12 questions at the end

Keep exploring

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Guide for grown-ups