How to use this page
Choose the chapter group you are studying. Each page will eventually include visuals and videos designed to help you see vectors, curves, surfaces, motion, partial derivatives, and multivariable integration.
The goal is to make three-dimensional calculus less like a collection of formulas and more like a set of visual stories about space, motion, shape, and accumulation.
Math 126 Chapter Groups
These pages are skeletons for now. Each will become a collection of visuals, interactives, videos, and guiding questions.
Chapter 12
Vectors and Geometry in 3DCoordinates in space, vectors, dot products, projections, cross products, lines, planes, and quadric surfaces.
Chapter 13
Curves in 3D and Motion in SpaceVector functions, space curves, velocity, acceleration, arc length, curvature, and motion through three-dimensional space.
Chapter 14
Partial Derivatives and OptimizationFunctions of several variables, level curves, surfaces, partial derivatives, tangent planes, linear approximation, critical points, and optimization.
Chapter 15
Double Integrals and Polar CoordinatesDouble integrals over rectangles and general regions, polar coordinates, center of mass, and accumulation over two-dimensional regions.
Taylor Polynomials and Series
Approximation and Infinite SeriesTaylor polynomials, error bounds, Taylor series, manipulating series, and using polynomials to approximate complicated functions.