Fall 2020 Online videos with steve butler

For each topic there are videos and scanned in notes. "Study guides" are linked to the videos so that clicking on any part of the study guide goes directly to that portion of the video.

These videos are currently in the process of being produced and are scheduled to be completed by October of 2020.

Brief overview of calculus

Cartesian coordinates; distance; spheres

Cylindrical and spherical coordinates

Vectors

Dot product

Cross product

Lines and planes

Quadric surfaces

Parametric curves

Motion and integration with parametric curves

Arc length; cumulative distance

Decomposing acceleration

Curvature

Multivariable functions

Limits of multivariable functions

Partial derivatives

Tangent planes; chain rule; implicit differentiation

Gradients; directional derivatives

Properties of the gradient; tangent planes; linearization

Taylor polynomials

Second partials test; optimization

Absolute max/min; optimization on closed and bounded sets

Lagrange multipliers; optimization with constraint

Multivariable integration (2D)

Changing order of integration (2D)

Integration in polar coordinates