Calculus III Videos

Below you can find Youtube links for my Calculus III lecture videos. While the videos are based on my lecture notes, the section numbers refer to the book Thomas’ Calculus, Early Transcendentals, 14th edition, by J. Hass, C. Heil, M.D. Weir (Pearson, 2018).

	Topic

12.	Vectors and the Geometry of Space

12.1	Coordinate Systems
12.2	Vectors
12.3	The Dot Product
12.4	The Cross Product
12.5	Lines and Planes in Space
12.6	Cylinders and Quadric Surfaces

13.	Vector-Valued Functions and Motion in Space

13.1	Curves in Space and Their Tangents
13.2	Integrals of Vector Functions and Projectile Motion
13.3	Arc Length in Space
13.4	Curvature and Normal Vectors of a Curve

14.	Partial Derivatives

14.1	Functions of Several Variables
14.2	Limits and Continuity in Higher Dimensions
14.3	Partial Derivatives
14.4	The Chain Rule
14.5	Directional Derivatives and Gradient Vectors
14.6	Tangent Planes
14.7	Extreme Values and Saddle Points
14.8	Lagrange Multipliers

15.	Multiple Integrals

15.1	Double Integrals over Rectangles
15.2	Double Integrals over General Domains
15.3	Area by Double Integration
15.4	Double Integrals in Polar Form
15.5	Triple Integrals in Rectangular Coordinates
15.7	Integrals in Cylindrical and Spherical Coordinates
15.8	Substitutions in Multiple Integrals

16.	Integrals and Vector Fields

16.1	Line Integrals of Scalar Functions
16.2	Vector Fields and Line Integrals
16.3	Path Independence and Conservative Vector Fields
16.4	Green’s Theorem in the Plane
16.5 - 16.8	Surface Integrals, Stokes’ Theorem, and the Divergence Theorem