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3.2 Multivariable Calculus
Continue your calculus journey into the realm of multiple variables, exploring everything from vectors to volume.
Searching Square Lake
Multivariable Limits
Shock Waves and Discontinuities
Extreme Value Theorem (Part I)
Extreme Value Theorem (Part II)
Basic Partial Derivatives
Higher-Order Partials
Under the Microscope: Tangent Planes
Directional Derivatives
The Gradient
Chain Rule of Several Variables
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)
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 — 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
- Extreme Value Theorem
- Gradient
- Hessian Test for Critical Points
- Jacobians & Variable Changes
- Lagrange Multipliers
- Limits and Continuity
- Multiple Integrals
- Multivariable Functions & Graphs
- Partial Derivatives
Prerequisites and next steps
You need to be familiar with multivariable functions, vectors and vector operations, and the basic ideas of calculus, including limits, derivatives, and integrals.
Up next
4.1 Introduction to Linear Algebra
Delve into the abstract depths of linear algebra: vector spaces, determinants, eigenvalues, wedge products, and more.
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