Multivariable Calculus· Study notes
Analysis
Calculus in two and three dimensions: vectors, curves, partial derivatives and optimization, multiple integrals, and the vector calculus of Green, Stokes and Gauss.
What you'll be able to do
- Differentiate and optimize functions of several variables
- Set up double and triple integrals in the right coordinates
- Compute line and surface integrals
- Apply the three big theorems
Read the notes as a guided lesson
Walk the notes one box at a time — prose, worked examples, quick checks — with a timed practice round after every section. For the full course with interactive lessons, go back to the course.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics
Lines & Planes in Space
5 lessonsNormals, distances, and intersections
Curves & Motion
5 lessonsVector-valued functions, speed, arc length, curvature
Partial Derivatives & the Gradient
5 lessonsSlopes in every direction at once
The Chain Rule & Implicit Differentiation
5 lessonsDependency trees, implicit curves, and Euler’s theorem
Optimization & Lagrange Multipliers
5 lessonsCritical points, the second-derivative test, constrained maxima
Double Integrals
5 lessonsVolume by slicing twice
Triple Integrals & Coordinate Systems
5 lessonsCylindrical and spherical coordinates
Change of Variables & the Jacobian
5 lessonsHow substitutions stretch area and volume
Vector Calculus
5 lessonsLine integrals, Green's theorem, div and curl
Surface Integrals, Stokes & Divergence
5 lessonsFlux through surfaces and the two capstone theorems