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Example: Real-world Application
by Carol Braun
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Formal Definition Of A Separable Differential Equation, And Example With Natural Logs
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Introduction To Solving Differential Equations By Separation Of Variables
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Example: Evaluating A Surface Integral When The Surface Is Given In Parametric Form
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Evaluating A Surface Integral When The Surface Is Given In Parametric Form
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Example: Converting To Polar Coordinates When Evaluating A Surface Integral For A Surface Given By z = g(x, y)
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Example: Evaluating A Surface Integral When Surface Is Given By z = g(x, y)
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Formula For Evaluating Surface Integrals When The Surface Is Given By z = g(x, y)
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Introduction To Surface Integrals
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Finding The Surface Area Of A Parametric Surface
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Example: Finding A Normal Vector And Tangent Plane To A Parametric Surface
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Finding The Normal Vector And Tangent Plane To A Parametric Surface
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Parametrizing A Surface Described By z = f(x, y)
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Example: Eliminating The Parameter To Sketch A Parametric Surface
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What Parametric Surfaces Are And Why We Use Them
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Parametric Equations For A Surface Of Revolution
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Example: Using Traces To Sketch The Graph Of A Parametric Surface
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Green's Theorem Extended To A Region With A Hole
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Using A Line Integral To Find An Area
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Example: Using Green's Theorem To Evaluate A Line Integral, And Verifying Green's Theorem
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Why Green's Theorem Is True, And Some Alternative Ways To Write Green's Theorem
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Introduction To Green's Theorem
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Differential Form For Line Integrals Of Vector Fields
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Example: Work Done By A Force Field
