Mr. Integral

THE BIG IDEA

Equations and Initial Values

What can a rate law tell us before we solve it?

A differential equation constrains how a quantity changes. Verify candidate curves, add initial data to identify a trajectory, and read a direction field to anticipate behavior before doing algebra.

Begin the first lesson →See the lesson route ↓

3 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Rate laws
  2. selecting a trajectory uses02Initial values
  3. evaluating local rates builds03Direction fields

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit3 lessons
  1. 01Differential Equations and Solution FamiliesTranslate a rate law into an equation and verify a proposed solution.
  2. 02Initial Values, Existence and UniquenessDecide what local existence and uniqueness guarantee, and what they do not.
  3. 03Direction Fields and Solution CurvesRead slopes from an equation before attempting an exact solution.