{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sn7_1 - Math 2433 Week 7 Popper007 1 Have you signed up for...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 2433 – Week 7 Popper007 1. Have you signed up for a time for your midterm yet? a. YES b. NO (then go do it NOW and come back and choose A) 2. Calculate the partial derivatives. a) b) c) d) e) 15.1 - DIFFERENTIABILITY AND GRADIENT We say that f is differentiable at x if there exists a vector y such that f ( x + h ) - f ( x ) = y i h + o ( h ). We will say that g ( h ) is o ( h ) if 0 (h) lim 0 h h g = Example: For 2 ( , ) 3 f x y x y = + :
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Let f be differentiable at x . The gradient of f at x is the unique vector f ( x ) such that f ( x + h ) - f ( x ) = f ( x ) i h + o ( h ). Continuing the previous example: More examples:
Image of page 2
Popper007 3. Find the gradient.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
15.2 Gradients and Directional Derivatives Properties of gradients: Directional Derivatives: Note that u f gives the rate of change of f in the direction of u . And
Image of page 4
Example: 1. Find the directional derivative at the point P in the direction indicated. 2 2 ( , ) 3 at P(1,1) in the direction of f x y x y = + i j
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Note that the directional derivative in a direction u is the component of the gradient vector in that direction.
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern