Directional Derivatives in the Plane

1 / 18

# Directional Derivatives in the Plane - PowerPoint PPT Presentation

Chapter 14. 14.5 Directional Derivatives and Gradient Vectors. Directional Derivatives in the Plane. The next map shows the contours on the area in New York. The tributary streams flow perpendicular to the contour.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Directional Derivatives in the Plane' - traci

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Directional Derivatives in the Plane
• The next map shows the contours on the area in New York. The tributary streams flow perpendicular to the contour.
• The streams are following paths of steepest descent so the water reach the river as quickly as possible.
• The instantaneous rate of change in a stream’s altitude above sea level has a particular direction.
• In this section why this “downhill” direction is perpendicular to the contours.

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Directional Derivatives in the Plane

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Directional Derivatives in the Plane
• Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Interpretation of the Directional Derivative

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

• Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

• Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves
• Example
• Any other way to find the equation of the tangent line?

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves
• Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Functions of Three Variables

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Functions of Three Variables
• Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Functions of Three Variables
• Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Homework 6
• Exercise 14.5, No. 15.
• Exercise 14.5, No. 22.
• Exercise 14.5, No. 31.
• Homeworks must not be submitted, but there will be a 15-minute short quiz in every lecture, asking 1-2 of the homework problems.
• Next short quiz: Next week, at 17.15.