Directional derivatives in the plane
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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.

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Directional Derivatives in the Plane

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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

Calculation and Gradients


Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Calculation and Gradients

  • Example


Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Calculation and Gradients


Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Calculation and Gradients

  • 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.


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