Lecture12_Double_integrals

Lecture12_Double_integrals - Double Integrals and Green's...

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1 Double Integrals and Green’s Theorem ± This unit is based on Sections 9.10 through 9.12 , Chapter 9. ± All assigned readings and exercises are from the textbook ± Objectives : Make certain that you can define, and use in context, the terms, concepts and formulas listed below: evaluate double integrals in Cartesian and polar Use double integrals to evaluate area, volume, center of mass, moment of inertia,…etc. use Green’s theorem to convert a line integral along a boundary of a into a double integral, and to convert a double integral to a line integral along the boundary of a region use Green’s theorem to evaluate line integrals, and to determine work, area and moment of inertia. ± Reading : Read Section 9.10 - 9.12, pages 505-524. ± Exercises : Complete problems
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2 ± The integral over the region R may be calculated by 2 successive integrations: ∫∫ R dxdy y x f ) , ( 2. Similarly, for integrating first over x and then over y ∫∫ ∫ ∫ = R
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Lecture12_Double_integrals - Double Integrals and Green's...

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