This course on multivariable calculus aims to teach students the concepts and applications of vectors, dot and cross products, vector-valued functions, partial derivatives, double and triple integrals, and coordinate systems such as polar, cylindrical, and spherical coordinates. The course covers topics like domains, graphs, distance formula, traces, level curves, tangent planes, differentials, and Lagrange's theorem. The teaching method involves pre-class videos and the use of an open textbook. This course is intended for learners interested in advancing their understanding of calculus in multiple dimensions.
Overview
Syllabus
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.
Taught by
The Math Repository
