Materials (Fall 2025)
Materials (Fall 2025)
The following are the materials that were generated for the Fall 2025 class given by Steve Butler.
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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 (Fall 2025) (Problems; written solutions; Vimeo; YouTube)
Practice exam (Fall 2024) (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 (scanned notes; Vimeo; YouTube)
(Oct 15) Lagrange multipliers (scanned notes; Vimeo; YouTube)
(Oct 17) Bonus problem for Lagrange multipliers (scanned notes; Vimeo; YouTube)
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 (Fall 2025) (Problems; written solutions; Vimeo; YouTube)
Practice exam (Fall 2024) (Problems; written solutions; Vimeo; YouTube)
(Oct 17) Iterated integration (scanned notes; Vimeo; YouTube)
(Oct 20) Changing order of integration (scanned notes; Vimeo; YouTube)
(Oct 27) Integration in polar coordinates (scanned notes; Vimeo; YouTube)
(Oct 29) Triple integrals (scanned notes; Vimeo; YouTube)
(Oct 31) Applications to physics (scanned notes; Vimeo; YouTube)
(Nov 3) Integration in cylindrical and spherical coordinates (scanned notes; Vimeo; YouTube)
(Nov 5) Changing coordinate systems for integration (2D) (scanned notes; Vimeo; YouTube)
(Nov 7) Changing coordinate systems for integration (3D)
(Nov 10) Vector valued functions
(Nov 12) Line integrals and work
(Nov 14) Line integrals of conservative functions
(Nov 17) Green's Theorem
(Nov 19) Surface area
(Nov 21) Surface integrals
(Dec 1) Stokes Theorem**
(Dec 8) Gauss's Divergence Theorem**
(Dec 10) Practice with the variations of Fundamental Theorem of Calculus**
Practice A (1-5) (Problems; written solutions; Vimeo; YouTube)
Practice B (6-8) (Problems; written solutions; Vimeo; YouTube)
Practice C (9-11) (Problems; written solutions; Vimeo; YouTube)
Practice D (12-14) (Problems; Vimeo; YouTube) [Taken from Fall 2024]
Practice exam (Fall 2025) (Problems; written solutions; Vimeo; YouTube)
Practice exam A (Fall 2024) (Problems; written solutions; Vimeo; YouTube)
Practice exam B (Fall 2024) (Problems; written solutions; Vimeo; YouTube)