Double Integrals: Iterated Integrals, Regions and Polar Form
Evaluate double integrals step by step: iterated integrals, Fubini's theorem, curved regions, switching the order and polar coordinates.
· 7 min read
Multivariable Calculus
Vectors, partial derivatives, gradients and multiple integrals for Calculus 3.
Gradient and Directional Derivatives: Formula and Examples
Learn what the gradient vector is, how to compute a directional derivative with a unit vector, and why the gradient points in the direction of steepest ascent.
· 7 min read
Lagrange Multipliers: Method, Intuition and Worked Examples
Learn the method of Lagrange multipliers for constrained optimization, why the gradients must be parallel, and how to solve the equations in worked examples.
· 8 min read
Partial Derivatives: Notation, Meaning and Worked Examples
Learn how to compute partial derivatives, what they mean as slopes of traces, how to find second partials and why Clairaut's theorem makes mixed partials equal.
· 7 min read
Vectors, Dot Product and Cross Product: A Clear Guide With Examples
Learn vector components and magnitude, the dot product and the angle between vectors, and the cross product and area, with fully worked examples.
· 7 min read
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