1222 views
Line Integrals Of Vector Fields
by Carol Braun
1223 views
Physical And Geometrical Interpretations Of Line Integrals: Total Mass, Total Length, And Lateral Surface Area
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Example: Line Integral When C Is Given As A Vector-valued Function
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Example: Line Integral Along A Piecewise Smooth Curve
Example: Evaluating A Line Integral With Different Parametrizations
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Evaluating A Line Integral As A Definite Integral By Parametrizing The Curve
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Introduction To Line Integrals
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Using The Curl To See If A 3D Vector Field Is Conservative, And (if So) Integrating To Find Its Potential Function
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Geometrical Significance Of The Curl
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Geometrical Significance Of The Divergence
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Introduction To The Divergence And Curl Of A Vector Field
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Checking That A 2D Vector Field Is Conservative And Finding Its Potential Function
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Example: Using A Given Potential Function To Show That All Inverse-square Fields Are Conservative
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Introduction To Conservative Vector Fields
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Sketching A 2D Vector Field From Its Equation
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Gradients Are Vector Fields
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Vector Fields As Vector-valued Functions Of 2 Or 3 Variables
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Scalar Fields And Vector Fields
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Differential Equations That Can Be Solved By Simple Integration
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Slope Fields
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Example: Finding A Particular Solution Consistent With Given Initial Conditions
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Solution Curves For First-order Differential Equations
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Solutions To Differential Equations
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Introduction To Differential Equations