Online lectures

The following material corresponds with online materials prepared by Steve Butler. Most topics have a "clickable" PDF study guide which opens up the corresponding video. The topics will usually consist of a few sessions including an overview (which discusses the ideas and techniques) and some worked problem set(s). Each session has a scanned in copy of the notes ("PDF") and is available in streaming from two different online platforms (either "Vimeo" or "YouTube").

For best results the overview for a given topic should be reviewed and then work some subset of the problems (focus on basic problems first, and then more challenging as time allows). When needed the videos will provide a walk-through explanation of the solution.

The material is still under construction and should be completed soon.

Brief overview of calculus

Cartesian coordinates; distance; spheres [PDF]

Cylindrical and spherical coordinates [PDF]

Vectors [PDF]

Dot product [PDF]

Cross product [PDF]

Lines and planes [PDF]

Quadric surfaces [PDF]

Parametric curves [PDF]

Motion and integration with parametric curves [PDF]

Arc length; cumulative arc length [PDF]

Decomposing acceleration [PDF]

Curvature [PDF]

Multivariable functions [PDF]

Limits of multivariable functions [PDF]

Partial derivatives [PDF]

Tangent planes; chain rule; implicit differentiation [PDF]

Gradients; directional derivatives [PDF]

Properties of the gradient; tangent planes; linearization [PDF]

Taylor polynomials [PDF]

Second partials test; optimization [PDF]

Absolute max/min; optimization on closed and bounded sets [PDF]

Lagrange multipliers; optimization with constraint [PDF]

Multivariable integration (2D) [PDF]

Changing order of integration (2D) [PDF]

Integration in polar coordinates [PDF]

Triple integrals; changing order of integration (3D)

Applications with geometry (surface area)

Applications with physics (mass; center of mass; moments)