Directional derivatives in the plane
This presentation is the property of its rightful owner.
Sponsored Links
1 / 18

Directional Derivatives in the Plane PowerPoint PPT Presentation


  • 90 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

Directional Derivatives in the Plane

An Image/Link below is provided (as is) to download presentation

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


Directional derivatives in the plane

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.


Directional derivatives in the plane1

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Directional Derivatives in the Plane


Directional derivatives in the plane2

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Directional Derivatives in the Plane

  • Example


Interpretation of the directional derivative

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Interpretation of the Directional Derivative


Calculation and gradients

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Calculation and Gradients


Calculation and gradients1

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Calculation and Gradients

  • Example


Calculation and gradients2

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Calculation and Gradients


Calculation and gradients3

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Calculation and Gradients

  • Example


Gradients and tangents to level curves

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves


Gradients and tangents to level curves1

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves


Gradients and tangents to level curves2

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?


Gradients and tangents to level curves3

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves


Gradients and tangents to level curves4

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Gradients and Tangents to Level Curves

  • Example


Functions of three variables

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Functions of Three Variables


Functions of three variables1

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Functions of Three Variables

  • Example


Functions of three variables2

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Functions of Three Variables

  • Example


Homework 6

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.


  • Login