This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

Consequences of Stokes' Theorem

More Stokes' Theorem

Simply connected regions

Extended Stokes' Theorem

Stokes' Theorem

Conservative fields and exact differentials

Line integral on a helix

Del and the product rule

Extended Gauss' Theorem

Flux and the divergence theorem

OCW Scholar: Multivariable Calculus

Integration in polar coordinates

Regions of integration

Changing the order of integration

Flux through a square

Gravity and a half-sphere

Moment of inertia of a cylinder

Extended Green's Theorem

Green's Theorem in normal form

Flux across a curve

Application of Green's theorem

Line integrals: path dependence

Line integrals: parametrization independence

Lagrange Multipliers

Lagrange multipliers

Gradient and directional derivative

Parametric curves: velocity, acceleration, length

Systems of linear equations

Distance of a point to a plane

Equations of planes

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