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∇f, ∇·F, ∇×F. The three ways the del operator acts on scalar and vector fields — with physical interpretations.

Every smooth function can be approximated by a polynomial. Taylor series quantifies exactly how well.

Green's, Stokes', and the Divergence Theorem are the crown jewels of vector calculus. Here's the full picture.

Double integrals extend single-variable integration to compute volumes, masses, and probabilities over 2D regions.

Moving from one variable to many — how limits, derivatives, and integrals extend to higher dimensions.

A partial derivative measures how a multivariable function changes as one input varies while all others are held fixed.

From computing volumes of revolution to work and centres of mass — integration applied to real problems.

What happens when the limits of integration reach infinity — or the integrand blows up? Improper integrals handle both.

The definite integral computes area. Here's how to set it up, compute it, and handle regions between curves.

u-substitution reverses the chain rule. Recognise the pattern and 90% of integrals become straightforward.