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Multivariable Calculus

11 topics · study sheets, quizzes, and tests.

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Go through each topic step by step, with 10 timed practice problems after every section.

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Topics

1.

Vectors in Space

Dot, cross, and the geometry they encode

StudyQuizUnit Test
2.

Lines & Planes in Space

Normals, distances, and intersections

StudyQuizUnit Test
3.

Curves & Motion

Vector-valued functions, speed, arc length, curvature

StudyQuizUnit Test
4.

Partial Derivatives & the Gradient

Slopes in every direction at once

StudyQuizUnit Test
5.

The Chain Rule & Implicit Differentiation

Dependency trees, implicit curves, and Euler’s theorem

StudyQuizUnit Test
6.

Optimization & Lagrange Multipliers

Critical points, the second-derivative test, constrained maxima

StudyQuizUnit Test
7.

Double Integrals

Volume by slicing twice

StudyQuizUnit Test
8.

Triple Integrals & Coordinate Systems

Cylindrical and spherical coordinates

StudyQuizUnit Test
9.

Change of Variables & the Jacobian

How substitutions stretch area and volume

StudyQuizUnit Test
10.

Vector Calculus

Line integrals, Green's theorem, div and curl

StudyQuizUnit Test
11.

Surface Integrals, Stokes & Divergence

Flux through surfaces and the two capstone theorems

StudyQuizUnit Test