Double Integrals: How to Evaluate Them Step by Step
Evaluate double integrals as iterated integrals, switch the order of integration, and use polar coordinates. Step-by-step worked examples.
Category: Multivariable
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Gradient and Directional Derivative: Formulas and Examples
The gradient ∇f collects partial derivatives; the directional derivative D_u f = ∇f · u gives the slope in any direction. Worked example and geometric meaning.
Partial Derivatives: How to Calculate Them (with Examples)
A partial derivative differentiates in one variable, holding the others constant. Notation, examples, second partials and Clairaut’s theorem.