1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 21

4. 2D case:

5. If or then 2 or 3D cases:

6. Several dimensions: U(x,y,z) Compact notation using vector del, or nabla: Another notation: Partial derivative is taken assuming all other arguments fixed

7. Geometric meaning of the gradient Direction of the steepest ascent; Magnitude : the slope in that direction Direction of the steepest descent Magnitude : the slope in that direction http://reynolds.asu.edu/topo_gallery/topo_gallery.htm

8. Given the potential energy function find the x and y components of the corresponding force.

9. Have a great day! Reading: Chapter 9 Hw: All Chapter 8 problems and exercises