gradient - THE GRADIENT Math21a Section 13.6: 2,8 Section:...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: THE GRADIENT Math21a Section 13.6: 2,8 Section: 13.7: 40, 42 Problem A: given g ( x, y, z ) = z − f ( x, y ). What is the relation between the gradient of g , a vector in space and the gradient of f , a vector in the plane? Describe it in general and explain it also with a simple example, where you can draw the level curves of f and the level surfaces of g . NABLA. The symbol ∇ is called ”Nabla”. GRADIENT. Define the gradient of a function f ( x, y ) as ∇ f ( x, y ) = ( f x ( x, y ) , f y ( x, y )) or ∇ f ( x, y, z ) = ( f x ( x, y, z ) , f y ( x, y, z ) , f z ( x, y, z )) if the function has three variables. ETYMOLOGY. The name ”Nabla” means ”Egyp- tion harp”. Its origin is believed to be related to the Hebrew word ”nevel”=harp which seems to have the same aramaic origin. REMINDER CHAIN RULE. The chain rule in multivariable calculus can be written more compactly as d dt f ( vector r ( t )) = ∇ f ( vector r ( t )) · vector r ′ ( t ) It looks like the one-dimensional chain rule, but the derivative...
View Full Document

This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

Ask a homework question - tutors are online