The bookUnit 3 · Calculus of Variations65 / 83

Isoperimetric problems

Why this is asked: Introduce a Lagrange multiplier, solve the modified Euler–Lagrange equation, then use the constraint plus boundary conditions to pin every constant.

Constrained variational problems

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Constrained extremals: the multiplier methodinteractive

Fixed perimeter, maximum area — set up with a Lagrange multiplier and solved.

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Open this in the full syllabus view · Unit 3