Course 09 · College

Calculus III

Multivariable calculus — extending the tools of calculus to higher dimensions.

Overview

What this course covers.

Calculus III extends single-variable calculus into three-dimensional space. Students master vectors, partial derivatives, multiple integrals, and the theorems of vector calculus. This is the course where calculus meets geometry and physics in a profound way.

PrerequisitesAP Calculus BC or equivalent (Calc II).

Next CourseDiff. Equations →

Curriculum

Topics & units.

Unit 1

Vectors & 3D Geometry

›Vectors in 2D and 3D
›Dot product & cross product
›Lines and planes in space
›Cylinders and quadric surfaces

Unit 2

Partial Derivatives

›Functions of several variables
›Partial derivatives & gradients
›Tangent planes & linear approximation
›Optimization with Lagrange multipliers

Unit 3

Multiple Integrals

›Double integrals over rectangles and general regions
›Triple integrals
›Change of variables (polar, cylindrical, spherical)
›Applications: volume, mass, center of mass

Unit 4

Vector Calculus

›Vector fields and line integrals
›Green's Theorem
›Surface integrals
›Stokes' and Divergence Theorems

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