## Functions of Several Variables

- Overview of Functions of Several Variables
- Example of Evaluating and finding the domain of a function of several variables
- Example #2 Find and Sketch domain of a function of several variables
- Example #3 Find and Sketch the domain of a function of several variables
- Example #4 Find the domain and Range of a function of several variables
- Example #1 of Sketching a 3D function and finding its domain and range
- Example #2 of Sketching a 3D function and finding its domain and range

## Limits and Continuity

- Overview of Continuity and Discontinuity
- Example #1 for proving a function is continuous or discontinuous
- Example #2 for proving a function is continuous or discontinuous

## Partial Derivatives

- Partial Differentiation Overview
- Example of how a function increases/decreases using partial derivatives
- Example #1 of Finding First Order Partial Derivatives
- Example #2 of Finding First Order Partial Derivatives
- Example #3 of Finding First Order Partial Derivatives
- Example #1 of finding slope of the tangent when a surface intersects a plane
- Example #2 of finding slope of the tangent when a surface intersects a plane
- Example of using partial derivatives to find the rate of change of volume
- Overview of Higher Order Partial Derivatives
- Example #1 of Finding Second Order Derivatives
- Example #2 of Finding Second Order Partial Derivatives
- Example of finding a Higher-Order Partial Derivative

## Tangent Planes and Linear Approximations

- Overview of Tangent Lines and Linear Approximation for Single Variable Calculus
- Overview of Tangent Planes and Linear Approximation for Multivariable Calculus
- Example #1 of finding Linear Approximation using a tangent line
- Example #2 of finding Linear Approximation using a tangent line
- Example #3 of using a linear approximation using a tangent line
- Example #4 of using a linear approximation using a tangent line
- Example #1 of finding Linear Approximation using the tangent plane
- Example #2 of finding Linear Approximation using a tangent plane
- Example of finding where a tangent plane is horizontal
- Overview of Differentiability in Multivariable Calculus
- Example of showing a function of two or more variables is differentiable
- Definition and Example for Finding the Total Differential of a Function
- Example of using the Total Differential in finding max error for a circular spa
- Example of using the Total Differential in finding max error for a rectangular box
- Example of using the Total Differential in estimating the amount of tin for a can

## Multivariable Chain Rule

- Overview of the Chain Rule for Single Variable Calculus
- Two Examples of using the chain rule for 2D
- Overview of the Two Cases of the Chain Rule for Multivariable Calculus
- Five Examples of using the chain rule for 3D
- Overview of the General Version of the Chain Rule with example
- Overview of Implicit Differentiation for 2D and 3D
- Proof of Implicit Differentiation for 3D
- Two Examples of Implicit Differentiation for 3D

## Directional Derivatives and Gradient Vectors

- What is a Directional Derivative?
- Definition of the directional derivative analytically and geometrically
- Three Examples of finding the Directional Derivative given a vector or angle
- Overview of the Gradient Vector and its importance
- Two examples of finding the maximum rate of change and its direction
- Overview and Equation of Tangent Planes to Level Surfaces
- Two Examples of writing an equation of a tangent plane to a surface and finding the normal line to the curve
- Recap of the Significance of the Gradient Vector

## Relative Extrema

- How did we find relative maximums and minimums in Calc 1?
- Example of finding relative/local extrema for single variable calculus
- How do we find relative maximums and minimums in Calc 3?
- Three Examples of finding relative/local extrema for functions of several variables
- Overview of Optimization for Multivariable Calculus
- One Example of optimization for a function of several variabales

## Absolute Extrema

- How did we find Absolute Maximums and Minimums in Calc 1?
- Example of finding Absolute extrema for single variable calculus
- How do we find Absolute Maximums and Minimums in Calc 3?
- Example of finding Absolute Extrema on a disk
- Example of finding Absolute Extrema on a rectangle

## Lagrange Multipliers

- Overview of how and why we use Lagrange Multipliers to find Absolute Extrema
- Steps for how to optimize a function using Lagrange multipliers
- Three Examples of finding absolute extrema using Lagrange multipliers