Multivariable Calculus View more

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

Book 44 Lessons

Introduction

Start

Many Variables in a Nutshell

Finding Extrema

Coordinates in 3D

3D Volumes

Vector Bootcamp

Vector Arithmetic

Vector Properties

Equations of Lines

Dot Product Definition and Properties

Matrices

Determinants

The Cross Product

Multivariable Functions

Multivariable Functions

Function Domains

Basic Graphing

Graphs by Slices

Contour Maps

Level Sets

Limits with Many Variables

Searching Square Lake

Multivariable Limits

Shock Waves and Discontinuities

Extreme Value Theorem (Part I)

Extreme Value Theorem (Part II)

Derivatives

Basic Partial Derivatives

Higher-Order Partials

Under the Microscope: Tangent Planes

Directional Derivatives

The Gradient

Chain Rule of Several Variables

Optimization

Local Maxima and Minima

Back Under the Microscope: Quadrics

Back Under the Microscope: Hessian Test

Boundary Extrema

Method of Lagrange

Application: Lagrange Multipliers

Global Maxima and Minima

More Hessians! (Optional)

Multiple Integrals

Double Integrals (Part I)

Double Integrals (Part II)

Fubini's Theorem (Part I)

Fubini's Theorem (Part II)

Multiple Integrals

Multiple Integrals Applications

Change of Variables

Cylindrical & Spherical Integrals

Course description

Change is an essential part of our world, and calculus helps us quantify it. The change that most interests us happens 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.

Multivariable calculus continues the story of calculus. Learn how tools like the derivative and integral generalize to functions depending on several independent variables, and discover some of the exciting new realms in physics and pure mathematics they unlock.

Topics covered

  • Chain Rule
  • Contour Maps & Level Sets
  • Extreme Value Theorem
  • Gradient
  • Hessian Test for Critical Points
  • Jacobians & Variable Changes
  • Lagrange Multipliers
  • Limits and Continuity
  • Multiple Integrals
  • Multivariable Functions & Graphs
  • Partial Derivatives
  • 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, basic trigonometric identities, limits, derivatives, and integrals.

Prerequisites

Next steps