Lectures 35 and 36 Vector Fields and Line Integral Circulation and Flux Calculus II Topic 5: Vectorial Calculus
Calculus II
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Fluid Mechanics
Calculus II
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Fluid Mechanics
Calculus II
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Physical Fields
Calculus II
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Gradient Fields
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Drawing Vector Fields
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Drawing Vector Fields
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Drawing Complex Vector Fields
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Drawing Complex Vector Fieds
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Two-Dimensional Vector Fields
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Simple Two-Dimensional Vector Fields
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Rotation Vector Fields
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Radial Vector Fields
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Radial Vector Fields
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Radial Vector Fields
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Radial and Rotation Vector Fields
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Radial Fields in Three Dimensions
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Simple Three-Dimensional Vector Fields
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Simple Three-Dimensional Fields
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Gradient Fields
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Examples of Gradient Fields
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Electrical Fields
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Example of Potential Field
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Line Integral
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Line Integral: Definition and Calculus
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Calculating Scalar Line Integrals
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Scalar Line Integral: Example
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Example of Scalar Line Integral
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Line Integral is Path Dependent
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But‌ Not Always
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Geometrical Application
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Physical Examples of Scalar Line Integrals
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Physical Example
đ?œŒ = đ?‘˜(1 − đ?‘§)
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Line Integral of a Field
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Evaluating the Line Integral of a Field
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Example
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Work: Simple Case
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Work: General Case
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Work along a Path
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Calculating Work
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Example
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Closed and Simple Curves
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Flow Integral and Circulation
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Circulation
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Circulation
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Find the Circulation đ?‘=
Calculus II
đ?‘Ľâˆ’đ?‘Ś đ?‘Ľ
đ?‘Ľ2 + đ?‘Ś2 = 1
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Calculating Circulation
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Flux across a Plane Closed Curve
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Flux across a Plane Closed Curve
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Trivial Examples
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Calculating Flux across a Closed Plane Curve
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Example of Flux across a Closed Plane Curve
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Find the Heat Flux across the Boundary of a Plate
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Homework
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