In-person lectures (Fall 2019)

The following material corresponds with in-person lectures given by Steve Butler during the Fall 2019 semester. 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").

Calculus review; Cartesian coordinates; distance spheres

Cylindrical and spherical coordinates

Vectors; magnitude; unit vectors; midpoint

Dot product; angle between vectors; projection; work

Cross product; area; volume

Lines; planes; normal vectors; distances

Quadric surfaces

Parametric curves; motion; derivatives of vector valued functions; tangent lines

Integrals of vector functions

Arc length; cumulative arc length

Decomposing motion; unit tangent; unit normal; unit binormal; osculating plane


Q&A for Exam 1

Functions of several variables; level curves; level surfaces; contour diagrams

Limits; continuity

Partial derivatives; higher order partial derivatives

Differentiability; tangent plane; chain rule; implicit differentiation

Gradient; directional derivative

Tangent planes; properties of gradient; linear approximation

Taylor polynomials for multivariable functions

Optimization; critical points; classification with second partials test

Optimization for a closed and bounded region

Optimization using method of Lagrange multipliers

Q&A for Exam 2

Multivariable integration; iterated integrals over rectangles and regions

Changing order of integration

Integration in polar coordinates

Triple integration in Cartesian coordinates; changing order of integration

Geometrical applications of multivariable integration

Physics applications of multivariable integration

Integration in cylindrical and spherical coordinates

Jacobian; substitution in multiple integrals

Vector fields; curl; divergence

Line integrals; work

Line integrals of conservative functions

Green's Theorem

Surface integrals

Q&A for Exam 3

Stokes' Theorem

Gauss's Divergence Theorem

Practice recognizing Stokes and Divergence