{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Engineering Calculus Notes 444

# Engineering Calculus Notes 444 - 432 CHAPTER 4 MAPPINGS AND...

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

432 CHAPTER 4. MAPPINGS AND TRANSFORMATIONS in other words, vector q ( s ) = vector p ( t ) dt ds . The second and third examples above have further generalizations in light of Theorem 4.2.5 . If f : R 3 R is a function defined on the surface S and −→ p ( s,t ) is a parametrization of S ( −→ p : R 2 R 3 ), then f −→ p expresses f as a function of the two parameters s and t , and the Chain Rule gives the partials of f with respect to them: setting −→ x = −→ p ( s,t ), Jf ( −→ x ) = bracketleftbigg ∂f ∂x ∂f ∂y ∂f ∂z bracketrightbigg J −→ p ( s,t ) = ∂x/∂s ∂x/∂t ∂y/∂s ∂y/∂t ∂z/∂s ∂z/∂t so J ( f −→ p )( s,t ) = Jf ( −→ x ) · J −→ p ( s,t ) = bracketleftbigg ∂f ∂x ∂x ∂s + ∂f ∂y ∂y ∂s + ∂f ∂z ∂z ∂s ∂f ∂x ∂x ∂t + ∂f ∂y ∂y ∂t + ∂f ∂z ∂z ∂t bracketrightbigg ; the first entry says
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern