{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

jacobianhandout - Jacobian Transformation Shubhodeep...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Jacobian Transformation Shubhodeep Mukherji May 22, 2011 1 Basics of Multi-Cal 1.1 Partial Derivative Given a function f , when taking the partial derivative with respect to one variable, treat all the other variables as constants. Example 1 Find ∂f ∂x and ∂f ∂y for the function f ( x, y ) = x 2 + 3 xy + y - 1 . 1.2 Fubini’s Theorem If f ( x, y ) is continuous throughout rectangular region R : a x b, c y d , then ZZ R f ( x, y ) dA = Z d c Z b a f ( x, y ) dxdy = Z b a Z d c f ( x, y ) dydx. 1.3 Finding Limits of Integration If calculating RR R f ( x, y ) dA first wrt y and then wrt x , do the following: 1. Sketch region of integration and label bounding curves 2. Find y-limits of integration 3. Find x-limits of integration Example 2 Calculate the area of region R bounded by the curves x 2 + y 2 = 1 and x + y = 1 . 1
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
2 Rotation 2.1 Mass and First Moment Formulas Mass: M = ZZ R δ ( x, y ) dA First Moments: M x = ZZ R ( x, y ) dA, M y = ZZ R ( x, y ) dA Center of Mass: x = M y M , y = M x M 2.2 Second Moment Formulas Second moment is rotational inertia.
Image of page 2
Image of page 3
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