Mr. Integral

THE BIG IDEA

Optimization in Several Variables

Where is the best value when movement has limits?

A stationary point is only a candidate. Use local curvature to classify it, inspect boundaries for global questions, and handle constraints through their geometry rather than ignoring them.

Begin the first lesson →See the lesson route ↓

4 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 with01Stationary points
  2. global extrema also require02Boundary candidates
  3. restricted motion leads to03Constraints
  4. local curvature improves04Quadratic models

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 unit4 lessons
  1. 01Critical Points and the HessianClassify stationary points using second-order behavior and recognize an inconclusive test.
  2. 02Absolute Extrema on Closed RegionsSearch interiors, edges and corners before comparing candidate values.
  3. 03Lagrange Multipliers and Constraint GeometryFind constrained candidates while checking regularity and the complete feasible set.
  4. 04Multivariable Taylor Approximation and ErrorUse a Hessian to improve a local model and bound error across all nearby directions.