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Calculus II Topic 5: Vectorial Calculus Calculus II Santiago de Vicente 1 Santiago de Vicente 2 Calculus II Santiago de Vicente 3 Calculus II Santiago de Vicente 4 Calculus II Santiago de Vicente 5 Calculus II Santiago de Vicente 6 Calculus II Santiago de Vicente 7 Calculus II Santiago de Vicente 8 Calculus II Santiago de Vicente 9 Calculus II Santiago de Vicente 10 Calculus II Santiago de Vicente 11 Calculus II Santiago de Vicente 12 Calculus II Santiago de Vicente 13 Calculus II
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Lectures 35 and 36 Vector Fields and Line Integral
Circulation and Flux
Calculus II
Topic 5: Vectorial Calculus
Calculus II Santiago de Vicente 1
Calculus II Santiago de Vicente 2
Fluid Mechanics
Calculus II Santiago de Vicente 3
Fluid Mechanics
Calculus II Santiago de Vicente 4
Physical Fields
Calculus II Santiago de Vicente 5
Gradient Fields
Calculus II Santiago de Vicente 6
Drawing Vector Fields
Calculus II Santiago de Vicente 7
Drawing Vector Fields
Calculus II Santiago de Vicente 8
Drawing Complex Vector Fields
Calculus II Santiago de Vicente 9
Drawing Complex Vector Fieds
Calculus II Santiago de Vicente 10
Two-Dimensional Vector Fields
Calculus II Santiago de Vicente 11
Simple Two-Dimensional Vector Fields
Calculus II Santiago de Vicente 12
Rotation Vector Fields
Calculus II Santiago de Vicente 13
Radial Vector Fields
Calculus II Santiago de Vicente 14
Radial Vector Fields
Calculus II Santiago de Vicente 15
Radial Vector Fields
Calculus II Santiago de Vicente 16
Radial and Rotation Vector Fields
Calculus II Santiago de Vicente 17
Radial Fields in Three Dimensions
Calculus II Santiago de Vicente 18
Simple Three-Dimensional Vector Fields
Calculus II Santiago de Vicente 19
Simple Three-Dimensional Fields
Calculus II Santiago de Vicente 20
Gradient Fields
Calculus II Santiago de Vicente 21
Examples of Gradient Fields
Calculus II Santiago de Vicente 22
Electrical Fields
Calculus II Santiago de Vicente 23
Example of Potential Field
Calculus II Santiago de Vicente 24
Line Integral
Calculus II Santiago de Vicente 25
Line Integral: Definition and Calculus
Calculus II Santiago de Vicente 26
Calculating Scalar Line Integrals
Calculus II Santiago de Vicente 27
Scalar Line Integral: Example
Calculus II Santiago de Vicente 28
Example of Scalar Line Integral
Calculus II Santiago de Vicente 29
Line Integral is Path Dependent
Calculus II Santiago de Vicente 30
But… Not Always
Calculus II Santiago de Vicente 31
Geometrical Application
Calculus II Santiago de Vicente 32
Physical Examples of Scalar Line Integrals
Calculus II Santiago de Vicente 33
Physical Example
𝜌 = 𝑘(1 − 𝑧)
Calculus II Santiago de Vicente 34
Line Integral of a Field
Calculus II Santiago de Vicente 35
Evaluating the Line Integral of a Field
Calculus II Santiago de Vicente 36
Example
Calculus II Santiago de Vicente 37
Work: Simple Case
Calculus II Santiago de Vicente 38
Work: General Case
Calculus II Santiago de Vicente 39
Work along a Path
Calculus II Santiago de Vicente 40
Calculating Work
Calculus II Santiago de Vicente 41
Example
Calculus II Santiago de Vicente 42
Closed and Simple Curves
Calculus II Santiago de Vicente 43
Flow Integral and Circulation
Calculus II Santiago de Vicente 44
Circulation
Calculus II Santiago de Vicente 45
Circulation
Calculus II Santiago de Vicente 46
Find the Circulation
𝑭 =𝑥 − 𝑦𝑥
𝑥2 + 𝑦2 = 1
Calculus II Santiago de Vicente 47
Calculating Circulation
Calculus II Santiago de Vicente 48
Flux across a Plane Closed Curve
Calculus II Santiago de Vicente 49
Flux across a Plane Closed Curve
Calculus II Santiago de Vicente 50
Trivial Examples
Calculus II Santiago de Vicente 51
Calculating Flux across a Closed Plane Curve
Calculus II Santiago de Vicente 52
Example of Flux across a Closed Plane Curve
Calculus II Santiago de Vicente 53
Find the Heat Flux across the Boundary of a Plate
Homework
Calculus II Santiago de Vicente 54