# Several Variables Calculus

This is an overview of several variable calculus.

### Format

• You should visit the sections below in order starting with Section 1.
• Each section below has several videos explaining the listed concepts, exercises with solution videos, and self-assessment questions.
• If you have watched the videos below and want to see more videos to better understand the material, you can see Chapter 14 of our course MATH 251: Several Variables Calculus. Note these MATH 251 videos are outside the scope of this mini-course and not required viewing.

## Several Variables Calculus

View Section 1: Functions of Several Variables
• ​The definition of a function of two variables
• The graph of a function of two variables with domain $$D$$ and range $$R$$
• The level curves of a function of two variables
View Section 2: Limits and Continuity
• Calculating the limit of a surface
• The definition of the limit of a two-variable function
• Limits at infinity and infinite limits of two-variable functions
View Section 3: Partial Derivatives
• ​The definition the partial derivative of $$f(x,y)$$ with respect to $$x$$ and $$y$$
• The geometric interpretation of the partial derivative
• Higher order partial derivatives and Clairaut’s Theorem
View Section 4: Tangent Planes and Linear Approximations
• ​The equation of the tangent plane
• Differentials
• Applications of differentials
View Section 5: The Chain Rule
• The chain rule for functions of more than one variable
• Related rates
View Section 6: Directional Derivatives and The Gradient Vector
• The Directional Derivative
View Section 7: Maximum and Minimum Values
• Local and absolute extrema of a function $$z = f (x, y)$$
• The Second Derivative Test for Local Extrema
• Extreme Value Theorem for Functions of Two Variables
View Section 8: Lagrange's Theorem
• Explanation of Lagrange's Theorem
• Finding the absolute maximum or absolute minimum values of $$z=f(x,y)$$ subject to a constraint $$g(x,y)=k$$