jacobian - Jacobian Transforma- tion Shubhodeep Mukherji...

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Unformatted text preview: Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Jacobian Transformation Shubhodeep Mukherji Multivariate Calculus Independent Study Science Academy of South Texas May 22, 2011 Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Partial Derivatives Math! Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Partial Derivatives Math! Use the symbol ∂ to distinguish partial derivative Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Partial Derivatives Math! Use the symbol ∂ to distinguish partial derivative Given a function f , when taking the partial derivative with respect to one variable, treat all the other variables as constants. Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Partial Derivatives Math! Use the symbol ∂ to distinguish partial derivative Given a function f , when taking the partial derivative with respect to one variable, treat all the other variables as constants. Example Find ∂ f ∂ x and ∂ f ∂ y for the function f ( x , y ) = x 2 + 3 xy + y- 1. Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Multiple Integrals Math! Same principle as for Partial Derivatives Example Z 3 Z 2 ( 4 x- y 2 ) dydx Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Area and Fubini’s Theorem Math! Area Area of a closed, bounded region R is A = ZZ R dA . Note: dA is called the ”‘area element”’ Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Area and Fubini’s Theorem Math! Area Area of a closed, bounded region R is A = ZZ R dA . Note: dA is called the ”‘area element”’ Fubini’s Theorem If f ( x , y ) is continuous throughout rectangular region R : a ≤ x ≤ b , c ≤ y ≤ d , then Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Area and Fubini’s Theorem Math! Area Area of a closed, bounded region R is A = ZZ R dA . Note: dA is called the ”‘area element”’ 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 . Jacobian Transforma- tion Shubhodeep Mukherji Basics of Multi-Cal Rotation Ellipse Problem Transformation Jacobian in Action Finding Limits of Integration Math!...
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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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jacobian - Jacobian Transforma- tion Shubhodeep Mukherji...

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