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Lectures 45 and 46 Three-Dimensional Divergence and Curl Gauss and Stokes Theorems Calculus II Topic 5: Vectorial Calculus

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Three Dimensional Divergence and Rotational

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Examples

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Divergence and Rotational in 3-D

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Example: Divergence for Radial Vector Fields

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Product Rule for Divergence

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Rotational of a Vector Field

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Circulation, Rotational and Orientation of a Surface

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Stokes Theorem

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2-D and 3-D Cases

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2-D and 3-D Stokes’ Theorem

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Examples of Stokes’ Theorem

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But,‌ is more intelligent to do something else

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Examples of Stokes’ Theorem

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But,‌ is more intelligent to do something else

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Another Example

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The last Example

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Exercise: Apply Stokes Theorem

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Important Remark

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Surfaces with Holes

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The Gauss Theorem

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2-D and 3-D Cases

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Example of Gauss Theorem

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Exercise: Check Gauss Theorem

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Gauss Theorem in Hollow Domains

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Example: Flux across a Hollow Region

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Gauss Law

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Gauss Law in Electrostatics

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Aopplications: Maxwell Laws in Electromagnetism

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Remember:

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Important Results

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Remember:

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Homework

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5.7_5.8_Teoremas_de_Gauss_y_Stokes_