# Multivariable Calculus

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

44 Lessons

## Multiple 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
• 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.