jacobianhandout - Jacobian Transformation Shubhodeep...

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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
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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:
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This note was uploaded on 08/03/2011 for the course ECON 101 taught by Professor Profeessor during the Spring '11 term at Aachen University of Applied Sciences.

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jacobianhandout - Jacobian Transformation Shubhodeep...

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