The A.L.L. Method - With Example: Lagrange Multipliers/Constrained Optimization

This is meant to be a blueprint for a revised lecture format for teaching any calculus class. This particular Instructable is using the example of teaching the Lagrange multiplier method of constrained optimization.

Supplies

- Notes for lecture on Lagrange Multipliers

Step 1:

Preliminary questions: introduce the concepts using a “what if” example.

Step 2:

Recap students on related/previous formula (2D) by asking guiding questions and use a suitable context and images

Step 3:

Introduce the core ideas of the Lagrange multiplier using a simple example and graphical representation

Step 4:

Derive the Lagrange multiplier formula and ask students question for them to participate while deriving (3D function)

Step 5:

Lead students to solve a simple example using derived formula, images and context is used to aid understanding

Step 6:

Lead students to solve a slightly more complex example, no image and little context is present

Step 7:

Ask students to give ideas about application of Lagrange multiplier, how is it useful, how is it used in real life.

Step 8:

Provide a recap of what has been covered in this class, with all important definitions and formulas

Step 9:

Assign self-reflection homework: Think of another situation in your major where you might use constrained optimization