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

2D case:

If or then 2 or 3D cases:

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

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

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

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