# 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

- 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

- 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

- The equation of the tangent plane
- Differentials
- Applications of differentials

- The chain rule for functions of more than one variable
- Related rates

- The Directional Derivative
- The gradient vector

- 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

- Explanation of Lagrange's Theorem
- Finding the absolute maximum or absolute minimum values of \(z=f(x,y)\) subject to a constraint \(g(x,y)=k\)