Multivariable Calculus

Materials (Fall 2025)

The following are the materials that were generated for the Fall 2025 class given by Steve Butler.

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(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]

(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) (scanned notes; Vimeo; YouTube)
(Nov 10) Vector valued functions (scanned notes; Vimeo; YouTube)
(Nov 12) Line integrals and work (scanned notes; Vimeo; YouTube)
(Nov 14) Line integrals of conservative functions (scanned notes; Vimeo; YouTube)
(Nov 17) Green's Theorem (scanned notes; Vimeo; YouTube)
(Nov 19) Surface area (scanned notes; Vimeo; YouTube)
(Nov 21) Surface integrals (scanned notes; Vimeo; YouTube)
(Dec 1) Stokes Theorem**
(Dec 8) Gauss's Divergence Theorem**
(Dec 10) Practice with the variations of Fundamental Theorem of Calculus**