Materials (Fall 2025)
Materials (Fall 2025)
The following are the materials that were generated for the Fall 2025 class given by Steve Butler.
Note: Vimeo is a video hosting service which streams a better quality video and has no ads.
The following are the materials that were generated for the Fall 2025 class given by Steve Butler.
Note: Vimeo is a video hosting service which streams a better quality video and has no ads.
(Aug 25) Cartesian coordinates; distance (scanned notes; Vimeo; YouTube)
(Aug 27) Cylindrical and spherical coordinates (scanned notes; Vimeo; YouTube)
(Aug 29) Vectors; unit vectors; midpoint (scanned notes; Vimeo; YouTube)
(Sep 3) Dot products; angles; projection (scanned notes; Vimeo; YouTube)
(Sep 5) Cross product; area/volume (scanned notes; Vimeo; YouTube)
(Sep 8) Lines; planes; normal; distance (scanned notes; Vimeo; YouTube)
(Sep 10) Quadric surfaces (scanned notes; Vimeo; YouTube)
(Sep 12) Parametric curves; tangents (scanned notes; Vimeo; YouTube)
(Sep 15) Integrals of vector functions (scanned notes; Vimeo; YouTube)
(Sep 17) (Cumulative) Arc length (scanned notes; Vimeo; YouTube)
(Sep 19) Decomposing motion; curvature (scanned notes; Vimeo; YouTube)
Practice A (1-3) (Problems; written solutions; Vimeo; YouTube)
Practice B (4-5) (Problems; written solutions; Vimeo; YouTube)
Practice C (6-8) (Problems; written solutions; Vimeo; YouTube)
Practice D (9-11) (Problems; Vimeo; YouTube) [Taken from Fall 2024.]
Practice exam (Problems; written solutions; Vimeo; YouTube)
(Sep 22) Multivariable functions (scanned notes; Vimeo; YouTube)
(Sep 29) Partial derivatives (scanned notes; Vimeo; YouTube)
(Oct 1) Differentiability; tangent planes; chain rule (scanned notes; Vimeo; YouTube)
(Oct 3) Implicit differentiation; gradient; directional derivatives (scanned notes; Vimeo; YouTube)
(Oct 6) Properties of the gradient; tangent planes (scanned notes; Vimeo; YouTube)
(Oct 8) Taylor polynomials (scanned notes; Vimeo; YouTube)
(Oct 10) Critical points; second partials test (scanned notes; Vimeo; YouTube)
(Oct 13) Absolute max/min
(Oct 15) Lagrange multipliers
Practice A (1-4) (Problems; written solutions; Vimeo; YouTube)
Practice B (5-7) (Problems; written solutions; Vimeo; YouTube)
Practice C (8-9) (Problems; Vimeo; YouTube) [Taken from Fall 2024]
Practice exam