Lectures 23 and 24 Double Integrals and Fubini’s Theorem Calculus II Topic 4: Multiple Integrals
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Notations
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Remembering the Concept of Riemann Integral of đ?‘“ đ?‘Ľ :
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đ?‘? đ?‘“ đ?‘Ž
đ?‘Ľ đ?‘‘đ?‘Ľ
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Double Integral as a Volume
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(1): Making a Grid Partition of Rectangular Region
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(2): Calculating Box Volumes
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(3): Making a Riemann Sum
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(4): Taking the Limit
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Riemann Double Integral on Rectangular Domains. Summary:
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Riemman Double Integral on Rectangular Domains and Volumes
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Integrability
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Integrability of Bounded Functions
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Calculating Volumes by Cavalieri’s Principle. The Slice Method
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Cavalieri’s Principle
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Cavalieri’s Principle: The Slice Method
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Application of Slice Method
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Slice Method Exercise
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Slice Method Exercise
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Application of Slice Method: Calculating Volumes of Revolution
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Slice Method on Both Directions đ?‘Ľ and đ?‘Ś
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Fubini’s Theorem
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Fubini’s Theorem for Bounded Functions
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Fubini’s Theorem Example
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Fubini’s Theorem Example
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Fubini’s Theorem Exercise
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Fubini’s Theorem Homework
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More Homework
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Average Value of a Function on a Rectangular Domain
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Example of Average Value of a Fuction of Two Variables
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Exercise of Average Value of a Two Variables Function
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Homework
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