serie a, f. 28
TRANSCRIPT
![Page 1: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/1.jpg)
Fascículo 28
N. A. Fava, G. Keilhauer, A. R. Larotonda
Cambio de variables, integrales de superficie y
coordenadas polares en Rn
Departamento de Matemática
Facultad de Ciencias Exactas y Naturales
Universidad de Buenos Aires
2011
ISSN 1853-709X
Cursos y seminarios de matemática
Serie A
![Page 2: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/2.jpg)
Cursos y Seminarios de Matemática – Serie A
Fascículo 28
Comité Editorial:
Carlos Cabrelli (Director) Departamento de Matemática, FCEyN, Universidad de Buenos Aires.E-mail: [email protected]
Gabriela JerónimoDepartamento de Matemática, FCEyN, Universidad de Buenos Aires.E-mail: [email protected]
Claudia Lederman Departamento de Matemática, FCEyN, Universidad de Buenos Aires. E-mail: [email protected]
Auxiliar editorial:
Leandro VendraminDepartamento de Matemática, FCEyN, Universidad de Buenos Aires. E-mail: [email protected]
ISSN 1853-709X (Versión Electrónica) ISSN 0524-9643 (Versión Impresa)
Derechos reservados© 2011 Departamento de Matemática, Facultad de Ciencias Exactas y Naturales,Universidad de Buenos Aires.
Departamento de MatemáticaFacultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresCiudad Universitaria – Pabellón I(1428) Ciudad de Buenos AiresArgentina.http://www.dm.uba.are-mail. [email protected]/fax: (+54-11)-4576-3335
![Page 3: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/3.jpg)
![Page 4: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/4.jpg)
![Page 5: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/5.jpg)
![Page 6: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/6.jpg)
![Page 7: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/7.jpg)
![Page 8: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/8.jpg)
![Page 9: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/9.jpg)
![Page 10: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/10.jpg)
![Page 11: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/11.jpg)
![Page 12: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/12.jpg)
![Page 13: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/13.jpg)
![Page 14: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/14.jpg)
![Page 15: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/15.jpg)
![Page 16: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/16.jpg)
![Page 17: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/17.jpg)
![Page 18: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/18.jpg)
![Page 19: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/19.jpg)
![Page 20: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/20.jpg)
![Page 21: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/21.jpg)
![Page 22: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/22.jpg)
![Page 23: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/23.jpg)
![Page 24: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/24.jpg)
![Page 25: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/25.jpg)
![Page 26: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/26.jpg)
![Page 27: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/27.jpg)
![Page 28: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/28.jpg)
![Page 29: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/29.jpg)
![Page 30: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/30.jpg)
![Page 31: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/31.jpg)
![Page 32: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/32.jpg)
![Page 33: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/33.jpg)
![Page 34: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/34.jpg)
![Page 35: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/35.jpg)
![Page 36: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/36.jpg)
![Page 37: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/37.jpg)
![Page 38: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/38.jpg)
![Page 39: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/39.jpg)
![Page 40: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/40.jpg)
![Page 41: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/41.jpg)
![Page 42: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/42.jpg)
![Page 43: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/43.jpg)
![Page 44: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/44.jpg)
![Page 45: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/45.jpg)
![Page 46: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/46.jpg)
![Page 47: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/47.jpg)
![Page 48: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/48.jpg)
![Page 49: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/49.jpg)
![Page 50: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/50.jpg)
![Page 51: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/51.jpg)
![Page 52: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/52.jpg)
![Page 53: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/53.jpg)
![Page 54: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/54.jpg)
![Page 55: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/55.jpg)
![Page 56: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/56.jpg)
![Page 57: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/57.jpg)
![Page 58: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/58.jpg)
![Page 59: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/59.jpg)
![Page 60: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/60.jpg)
![Page 61: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/61.jpg)
![Page 62: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/62.jpg)
![Page 63: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/63.jpg)
![Page 64: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/64.jpg)
![Page 65: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/65.jpg)
![Page 66: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/66.jpg)
![Page 67: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/67.jpg)
![Page 68: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/68.jpg)
![Page 69: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/69.jpg)
![Page 70: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/70.jpg)
![Page 71: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/71.jpg)
![Page 72: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/72.jpg)
![Page 73: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/73.jpg)
![Page 74: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/74.jpg)
![Page 75: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/75.jpg)
![Page 76: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/76.jpg)
![Page 77: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/77.jpg)
![Page 78: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/78.jpg)
![Page 79: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/79.jpg)
![Page 80: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/80.jpg)
![Page 81: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/81.jpg)
![Page 82: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/82.jpg)
![Page 83: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/83.jpg)
![Page 84: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/84.jpg)
![Page 85: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/85.jpg)
![Page 86: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/86.jpg)
![Page 87: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/87.jpg)
![Page 88: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/88.jpg)
![Page 89: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/89.jpg)
![Page 90: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/90.jpg)
![Page 91: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/91.jpg)
![Page 92: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/92.jpg)
![Page 93: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/93.jpg)
![Page 94: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/94.jpg)
![Page 95: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/95.jpg)
![Page 96: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/96.jpg)
![Page 97: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/97.jpg)
![Page 98: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/98.jpg)
![Page 99: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/99.jpg)
![Page 100: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/100.jpg)
![Page 101: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/101.jpg)
![Page 102: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/102.jpg)
![Page 103: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/103.jpg)
![Page 104: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/104.jpg)
![Page 105: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/105.jpg)
![Page 106: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/106.jpg)
![Page 107: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/107.jpg)
![Page 108: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/108.jpg)
![Page 109: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/109.jpg)
![Page 110: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/110.jpg)
![Page 111: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/111.jpg)
![Page 112: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/112.jpg)
![Page 113: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/113.jpg)
![Page 114: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/114.jpg)
![Page 115: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/115.jpg)
![Page 116: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/116.jpg)
![Page 117: Serie A, f. 28](https://reader034.vdocument.in/reader034/viewer/2022042605/587515521a28abab268c012e/html5/thumbnails/117.jpg)