1. Dr.-Ing. Erwin Sitompul President University Lecture 6 Multivariable Calculus President UniversityErwin SitompulMVC 6/1 http://zitompul.wordpress.com

2. President UniversityErwin SitompulMVC 6/2 Directional Derivatives in the Plane Chapter 1414.5 Directional Derivatives and Gradient Vectors 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.

3. President UniversityErwin SitompulMVC 6/3 Directional Derivatives in the Plane Chapter 1414.5 Directional Derivatives and Gradient Vectors

4. President UniversityErwin SitompulMVC 6/4 Directional Derivatives in the Plane Example Chapter 1414.5 Directional Derivatives and Gradient Vectors

5. President UniversityErwin SitompulMVC 6/5 Interpretation of the Directional Derivative Chapter 1414.5 Directional Derivatives and Gradient Vectors

6. President UniversityErwin SitompulMVC 6/6 Calculation and Gradients Chapter 1414.5 Directional Derivatives and Gradient Vectors

7. President UniversityErwin SitompulMVC 6/7 Calculation and Gradients Chapter 1414.5 Directional Derivatives and Gradient Vectors Example

8. President UniversityErwin SitompulMVC 6/8 Calculation and Gradients Chapter 1414.5 Directional Derivatives and Gradient Vectors

9. President UniversityErwin SitompulMVC 6/9 Calculation and Gradients Chapter 1414.5 Directional Derivatives and Gradient Vectors Example

10. President UniversityErwin SitompulMVC 6/10 Gradients and Tangents to Level Curves Chapter 1414.5 Directional Derivatives and Gradient Vectors

11. President UniversityErwin SitompulMVC 6/11 Gradients and Tangents to Level Curves Chapter 1414.5 Directional Derivatives and Gradient Vectors

12. President UniversityErwin SitompulMVC 6/12 Gradients and Tangents to Level Curves Chapter 1414.5 Directional Derivatives and Gradient Vectors Example Any other way to find the equation of the tangent line?

13. President UniversityErwin SitompulMVC 6/13 Gradients and Tangents to Level Curves Chapter 1414.5 Directional Derivatives and Gradient Vectors

14. President UniversityErwin SitompulMVC 6/14 Gradients and Tangents to Level Curves Chapter 1414.5 Directional Derivatives and Gradient Vectors Example

15. President UniversityErwin SitompulMVC 6/15 Functions of Three Variables Chapter 1414.5 Directional Derivatives and Gradient Vectors

16. President UniversityErwin SitompulMVC 6/16 Functions of Three Variables Chapter 1414.5 Directional Derivatives and Gradient Vectors Example

17. President UniversityErwin SitompulMVC 6/17 Functions of Three Variables Chapter 1414.5 Directional Derivatives and Gradient Vectors Example

18. President UniversityErwin SitompulMVC 6/18 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. Chapter 1414.5 Directional Derivatives and Gradient Vectors