Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4....
10
2/22/02 47 Week 4. Double integrals in polar coordinates
Transcript of Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4....
![Page 1: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/1.jpg)
2/22/02 47
Week 4. Double integralsin polar coordinates
![Page 2: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/2.jpg)
2/22/02 48
Week 4. Double integralsin polar coordinates, heuristics
Cartesian coordinates Polar coordinates
![Page 3: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/3.jpg)
2/22/02 49
Week 4. Double integrals to iteratedintegrals by polar coordinates
Fubini’s Theorem in polar coordinates
Sometimes such adomain is calleda polar rectangle.
![Page 4: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/4.jpg)
2/22/02 50
Week 4. Integrating with polarcoordinates, an example
![Page 5: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/5.jpg)
2/22/02 51
Week 4. The area of a domain
![Page 6: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/6.jpg)
2/22/02 52
Week 4. An example, the area, a
![Page 7: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/7.jpg)
2/22/02 53
Week 4. An example, the area, b
![Page 8: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/8.jpg)
2/22/02 54
Week 4. Physical applications:mass, first moments
(impulsmoment)
![Page 9: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/9.jpg)
2/22/02 55
Week 4. Physical applications:the center of mass
(zwaartepunt)
![Page 10: Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem](https://reader035.fdocuments.in/reader035/viewer/2022070804/5f0341937e708231d4084fc4/html5/thumbnails/10.jpg)
2/22/02 56
Week 4. Physical applications:second moments
(traagheidsmoment)