5.1_5.2_campos_integral_de_linea_

Lectures 35 and 36 Vector Fields and Line Integral

Circulation and Flux

Calculus II

Topic 5: Vectorial Calculus

Calculus II Santiago de Vicente 1


Fluid Mechanics


Physical Fields


Gradient Fields


Drawing Vector Fields


Drawing Complex Vector Fields


Drawing Complex Vector Fieds


Two-Dimensional Vector Fields


Simple Two-Dimensional Vector Fields


Rotation Vector Fields


Radial Vector Fields


Radial and Rotation Vector Fields


Radial Fields in Three Dimensions


Simple Three-Dimensional Vector Fields


Simple Three-Dimensional Fields


Gradient Fields


Examples of Gradient Fields


Electrical Fields


Example of Potential Field


Line Integral


Line Integral: Definition and Calculus


Calculating Scalar Line Integrals


Scalar Line Integral: Example


Example of Scalar Line Integral


Line Integral is Path Dependent


But… Not Always


Geometrical Application


Physical Examples of Scalar Line Integrals


Physical Example

𝜌 = 𝑘(1 − 𝑧)


Line Integral of a Field


Evaluating the Line Integral of a Field


Example


Work: Simple Case


Work: General Case


Work along a Path


Calculating Work


Example


Closed and Simple Curves


Flow Integral and Circulation


Circulation


Find the Circulation

𝑭 =𝑥 − 𝑦𝑥

𝑥2 + 𝑦2 = 1


Calculating Circulation


Flux across a Plane Closed Curve


Trivial Examples


Calculating Flux across a Closed Plane Curve


Example of Flux across a Closed Plane Curve


Find the Heat Flux across the Boundary of a Plate

Homework


5.1_5.2_campos_integral_de_linea_

Documents

vectorial calculus calculus

example calculus

flux calculus

path calculus

dimensions calculus

dependent calculus

physical fields calculus

electrical fields calculus