Lectures 28 and 29 Triple Integrals in Cartesian and Cylindrical Coordinates Calculus II Topic 4: Multiple Integrals

Calculus II

Santiago de Vicente

1

Building Triple Riemann Integral (1): Making a Partition of a Solid

Calculus II

Santiago de Vicente

2

Building Triple Riemann Integral (2): Making a Riemann Sum

Calculus II

Santiago de Vicente

3

Building Triple Riemann Integral (3): Taking the Limit

Calculus II

Santiago de Vicente

4

Calculating Triple Integrals

Calculus II

Santiago de Vicente

5

Calculating Triple Integrals (Fubiniâ&#x20AC;&#x2122;s Theorem)

Calculus II

Santiago de Vicente

6

Calculating Triple Integrals (Fubiniâ&#x20AC;&#x2122;s Theorem)

Calculus II

Santiago de Vicente

7

Fubiniâ&#x20AC;&#x2122;s Theorem

Calculus II

Santiago de Vicente

8

Volume and Average Value

Calculus II

Santiago de Vicente

9

Simple Example

Calculus II

Santiago de Vicente

10

Volume of a Sphere

Calculus II

Santiago de Vicente

11

Volume of a Witch Pot as Double and Triple Integral

Calculus II

Santiago de Vicente

12

Volume of a Wedge

Calculus II

Santiago de Vicente

13

Volume of a Wedge

Calculus II

Santiago de Vicente

14

The Volume of something as an Ice Cream

Calculus II

Santiago de Vicente

15

More Paraboloids

Calculus II

Santiago de Vicente

16

Changing Order of Integration

Calculus II

Santiago de Vicente

17

Changing Order of Integration

Calculus II

Santiago de Vicente

18

More Tetrahedron

Calculus II

Santiago de Vicente

19

Changing Order of Integration

Calculus II

Santiago de Vicente

20

Rememberign Cylindrical Coordinates

Calculus II

Santiago de Vicente

21

Typical Application

Calculus II

Santiago de Vicente

22

Typical Applications

Calculus II

Santiago de Vicente

23

Constant Coordinates and Volume Element in Cylindrical Coordinates

Calculus II

Santiago de Vicente

24

Fubiniâ&#x20AC;&#x2122;s Theorem in Cylindrical Coordinates

Calculus II

Santiago de Vicente

25

Change of Variables: Cartesian to Cylindrical

Calculus II

Santiago de Vicente

26

Examples

Calculus II

Santiago de Vicente

27

Internal Energy of a Salt in a Tank with knownTemperature Distribution

đ?&#x2018;&#x2021; đ?&#x2018;Ľ, đ?&#x2018;Ś, đ?&#x2018;§ = 1 + đ?&#x2018;Ľ 2 + đ?&#x2018;Ś 2 đ?&#x2018;&#x2026;đ?&#x2018;&#x17D;đ?&#x2018;&#x2018;đ?&#x2018;&#x2013;đ?&#x2018;˘đ?&#x2018; = 2 2 and đ?&#x2018;§ â&#x2C6;&#x2C6; â&#x2C6;&#x2019;1,2

Calculus II

Santiago de Vicente

28

Mass of a Storage of Porous Packed Material đ?&#x153;&#x152; đ?&#x2018;Ľ, đ?&#x2018;Ś, đ?&#x2018;§ = 5 â&#x2C6;&#x2019; đ?&#x2018;§

Calculus II

Santiago de Vicente

29

Volume of a Peg-Top

Calculus II

Santiago de Vicente

30

Homework

Calculus II

Santiago de Vicente

31

4.6_4.7_Integral_Triple_Cartesianas_Cilindricas

Calculus II Topic 4: Multiple Integrals Calculus II Santiago de Vicente 1 Santiago de Vicente 2 Calculus II Santiago de Vicente 3 Calculus I...