Multivariable Calculus

Explore comprehensive pre-class videos for multivariable calculus, designed to complement the open textbook "Active Multivariable Calculus." Delve into topics such as domains and graphs, vectors, dot and cross products, lines and planes in space, vector-valued functions, partial derivatives, tangent planes, the chain rule, double and triple integrals, and coordinate systems. Master concepts like limits, continuity, arc length, curvature, gradient, and Lagrange's theorem. Apply your knowledge to real-world scenarios involving areas, masses, center of mass, and joint probability density functions. Enhance your understanding of calculus in multiple dimensions through these in-depth video lessons, perfect for self-study or as a supplement to formal coursework.

9.1-1 - Domains and Graphs.
9.1-2 - The Distance Formula and the Equation of the Sphere.
9.1-3 - Traces and Level Curves.
9.2-1 - Introduction to Vectors.
9.2-2 - The Arithmetic of Vectors.
9.2-3 - The Magnitude of Vectors.
9.3-1 - Introduction to the Dot Product.
9.3-2 - Applications of the Dot Product.
9.4-1 - Introduction to the Cross Product.
9.4-2 - Properties of the Cross Product.
9.5-1 - Lines in Space.
9.5-2 - Planes in Space.
9.6-1 - Vector Valued Functions.
9.7-1 - Derivatives of Vector Functions.
9.7-2 - Integrals and Projectile Motion.
9.8-1 - Arc Length and the Arc Length Parameter.
9.8-2 - Curvature.
10.1-1 - Limits and Continuity.
10.2-1 - First Order Partial Derivatives.
10.3-1 - Second Order Partial Derivatives.
10.4-1 - Tangent Planes.
10.4-2 - Differentials.
10.5-1 - The Chain Rule.
10.6-1 - The Directional Derivative.
10.6-2 - The Gradient.
10.7-1 - First and Second Derivative Tests.
10.7-2 - Restricted Domains.
10.8-1 - Lagrange's Theorem.
11.1-1 - Double Integrals over Rectangles.
11.2-1 - Iterated Integrals.
11.3-1 - Double Integrals over General Regions.
11.4-1 - Areas and Masses.
11.4-2 - Center of Mass.
11.4-3 - Joint Probability Density Functions.
11.5-1 - Polar Coordinates.
11.6-1 - Parametric Surfaces and Surface Area.
11.7-1 - Triple Integrals.
11.8-1 - Cylindrical Coordinates.
11.8-2 - Spherical Coordinates.
11.9-1 - Change of Variables.