Lectures 45 and 46 Three-Dimensional Divergence and Curl Gauss and Stokes Theorems Calculus II Topic 5: Vectorial Calculus

Calculus II

Santiago de Vicente

1

Three Dimensional Divergence and Rotational

Calculus II

Santiago de Vicente

2

Examples

Calculus II

Santiago de Vicente

3

Divergence and Rotational in 3-D

Calculus II

Santiago de Vicente

4

Example: Divergence for Radial Vector Fields

Calculus II

Santiago de Vicente

5

Product Rule for Divergence

Calculus II

Santiago de Vicente

6

Rotational of a Vector Field

Calculus II

Santiago de Vicente

7

Circulation, Rotational and Orientation of a Surface

Calculus II

Santiago de Vicente

8

Stokes Theorem

Calculus II

Santiago de Vicente

9

2-D and 3-D Cases

Calculus II

Santiago de Vicente

10

2-D and 3-D Stokesâ&#x20AC;&#x2122; Theorem

Calculus II

Santiago de Vicente

11

Examples of Stokesâ&#x20AC;&#x2122; Theorem

Calculus II

Santiago de Vicente

12

But,â&#x20AC;Ś is more intelligent to do something else

Calculus II

Santiago de Vicente

13

Examples of Stokesâ&#x20AC;&#x2122; Theorem

Calculus II

Santiago de Vicente

14

But,â&#x20AC;Ś is more intelligent to do something else

Calculus II

Santiago de Vicente

15

Another Example

Calculus II

Santiago de Vicente

16

The last Example

Calculus II

Santiago de Vicente

17

Exercise: Apply Stokes Theorem

Calculus II

Santiago de Vicente

18

Important Remark

Calculus II

Santiago de Vicente

19

Surfaces with Holes

Calculus II

Santiago de Vicente

20

The Gauss Theorem

Calculus II

Santiago de Vicente

21

2-D and 3-D Cases

Calculus II

Santiago de Vicente

22

Example of Gauss Theorem

Calculus II

Santiago de Vicente

23

Exercise: Check Gauss Theorem

Calculus II

Santiago de Vicente

24

Gauss Theorem in Hollow Domains

Calculus II

Santiago de Vicente

25

Example: Flux across a Hollow Region

Calculus II

Santiago de Vicente

26

Gauss Law

Calculus II

Santiago de Vicente

27

Gauss Law in Electrostatics

Calculus II

Santiago de Vicente

28

Aopplications: Maxwell Laws in Electromagnetism

Calculus II

Santiago de Vicente

29

Remember:

Calculus II

Santiago de Vicente

30

Important Results

Calculus II

Santiago de Vicente

31

Remember:

Calculus II

Santiago de Vicente

32

Homework

Calculus II

Santiago de Vicente

33

5.7_5.8_Teoremas_de_Gauss_y_Stokes_

Calculus II Topic 5: Vectorial Calculus Lectures 45 and 46 Calculus II Santiago de Vicente 1 Santiago de Vicente 2 Calculus II Santiago de V...