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Multivariable Calculus

Analysis

Calculus in two and three dimensions: vectors, curves, partial derivatives and optimization, multiple integrals, and the vector calculus of Green, Stokes and Gauss.

11 topics · 56 lessons about 22 hoursBefore this: Calculus

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

Start the course

Go through each topic step by step — prose, worked examples, quick checks, and a timed practice round after every section.

Start
Final Test (30) Big Test (50) Search & glossary Flashcards Print the course (PDF)Suggest a problem

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

1.

Vectors in Space

6 lessons

Dot, cross, and the geometry they encode

Study PracticeQuizUnit TestTest out
2.

Lines & Planes in Space

5 lessons

Normals, distances, and intersections

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3.

Curves & Motion

5 lessons

Vector-valued functions, speed, arc length, curvature

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4.

Partial Derivatives & the Gradient

5 lessons

Slopes in every direction at once

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5.

The Chain Rule & Implicit Differentiation

5 lessons

Dependency trees, implicit curves, and Euler’s theorem

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6.

Optimization & Lagrange Multipliers

5 lessons

Critical points, the second-derivative test, constrained maxima

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7.

Double Integrals

5 lessons

Volume by slicing twice

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8.

Triple Integrals & Coordinate Systems

5 lessons

Cylindrical and spherical coordinates

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9.

Change of Variables & the Jacobian

5 lessons

How substitutions stretch area and volume

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10.

Vector Calculus

5 lessons

Line integrals, Green's theorem, div and curl

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11.

Surface Integrals, Stokes & Divergence

5 lessons

Flux through surfaces and the two capstone theorems

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