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President UniversityErwin SitompulMVC 6/3 Directional Derivatives in the Plane Chapter Directional Derivatives and Gradient Vectors
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Dr.-Ing. Erwin SitompulPresident University
Lecture 6
Multivariable Calculus
President University Erwin Sitompul MVC 6/1
http://zitompul.wordpress.com
President University Erwin Sitompul MVC 6/2
Directional Derivatives in the PlaneChapter 14 14.5 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.
President University Erwin Sitompul MVC 6/3
Directional Derivatives in the PlaneChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/4
Directional Derivatives in the Plane Example
Chapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/5
Interpretation of the Directional DerivativeChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/6
Calculation and GradientsChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/7
Calculation and GradientsChapter 14 14.5 Directional Derivatives and Gradient Vectors
Example
President University Erwin Sitompul MVC 6/8
Calculation and GradientsChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/9
Calculation and GradientsChapter 14 14.5 Directional Derivatives and Gradient Vectors
Example
President University Erwin Sitompul MVC 6/10
Gradients and Tangents to Level CurvesChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/11
Gradients and Tangents to Level CurvesChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/12
Gradients and Tangents to Level CurvesChapter 14 14.5 Directional Derivatives and Gradient Vectors
Example
Any other way to find the equation of the tangent line?
President University Erwin Sitompul MVC 6/13
Gradients and Tangents to Level CurvesChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/14
Gradients and Tangents to Level CurvesChapter 14 14.5 Directional Derivatives and Gradient Vectors
Example
President University Erwin Sitompul MVC 6/15
Functions of Three VariablesChapter 14 14.5 Directional Derivatives and Gradient Vectors
President University Erwin Sitompul MVC 6/16
Functions of Three VariablesChapter 14 14.5 Directional Derivatives and Gradient Vectors
Example
President University Erwin Sitompul MVC 6/17
Functions of Three VariablesChapter 14 14.5 Directional Derivatives and Gradient Vectors
Example
President University Erwin Sitompul MVC 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 14 14.5 Directional Derivatives and Gradient Vectors
