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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.

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Directional Derivatives in the Plane

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  1. 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.

  2. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Directional Derivatives in the Plane

  3. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Directional Derivatives in the Plane • Example

  4. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Interpretation of the Directional Derivative

  5. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Calculation and Gradients

  6. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Calculation and Gradients • Example

  7. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Calculation and Gradients

  8. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Calculation and Gradients • Example

  9. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Gradients and Tangents to Level Curves

  10. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Gradients and Tangents to Level Curves

  11. 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?

  12. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Gradients and Tangents to Level Curves

  13. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Gradients and Tangents to Level Curves • Example

  14. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Functions of Three Variables

  15. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Functions of Three Variables • Example

  16. Chapter 14 14.5 Directional Derivatives and Gradient Vectors Functions of Three Variables • Example

  17. 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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