Section 14.1 Functions of Several Variables

• Functions of Several Variables
• Level Curves

Section 14.2 Limits and Continuity

• Limits of Surfaces
• Continuity
• Squeeze Theorem Example

Section 14.3 Partial Derivatives

• Partial Derivatives
• Higher Order Derivatives
• Production Function Application
• Implicit Differentiation Example

Section 14.4 Tangent Planes and Linear Approximations

• Tangent Planes
• Linearization
• Differentials

Section 14.5 The Chain Rule

• The Chain Rule – Main Idea
• Related Rates Example
• The General Chain Rule
• Another General Chain Rule Example
• Partial Differential Equation Proof
• Implicit Differentiation

Section 14.6 Directional Derivatives and the Gradient Vector

• Directional Derivatives – The Main Idea
• Maximizing Directional Derivatives
• Crawling Bug Problem
• Tangent Planes to Level Surfaces

Section 14.7 Maximum and Minimum Values

• Max and Min Values – The Main Idea
• Second Derivative Test
• More Examples with Extrema
• Absolute Extrema

Section 14.8 Lagrange Multipliers

• Lagrange Multipliers  – The Main Idea
• Max Volume of a Box Example
• Soda Can Example
• Optimizing f given Multiple Constraints