Advanced Math · Level 3

3.1 Multivariable Functions

Discover the multi-dimensional space of multivariable functions, and learn how to think about scenarios with more than one changing parameter.

Many Variables in a Nutshell

Finding Extrema

Coordinates in 3D

3D Volumes

Vector Arithmetic

Vector Properties

Equations of Lines

Dot Product Definition and Properties



The Cross Product

Multivariable Functions

Function Domains

Basic Graphing

Graphs by Slices

Contour Maps

Level Sets

Course description

Most interesting things occur in systems with more than one variable: weather depends on time of year and location on the Earth, economies have several sectors, important chemical reactions have many reactants and products. This course unpacks the unique characteristics of functions that have more than one variable and the tools needed to think about them.

Topics covered

  • 3D Coordinates
  • Contour Maps
  • Cross Product
  • Determinants
  • Dot Product
  • Level Sets
  • Vectors and Matrices

Prerequisites and next steps

You’ll need an understanding of algebra and the basics of functions, such as domain and range, graphs, and intercepts. You should also be familiar with exponential functions, logarithms, and basic trigonometric identities.

Up next

Advanced Math · Level 3

3.2 Multivariable Calculus

Continue your calculus journey into the realm of multiple variables, exploring everything from vectors to volume.

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