{"title":"斯托克斯公式","authors":"C. E. Gutiérrez","doi":"10.1142/9789811222573_0007","DOIUrl":null,"url":null,"abstract":"Here curlnF(P) is defined as follows. Let P ∈ R3 and n be a unit vector and let S be a surface through P having normal n at P. Consider a closed curve C contained in S and circulating counterclockwise around the point P, and let A be the area of the portion of surface enclosed by C. Then curlnF(P) is the limit of the ratio between the line integral of F over C over the area of A when C shrinks to P, that is,","PeriodicalId":114943,"journal":{"name":"Basic Insights in Vector Calculus","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"STOKES’ THEOREM\",\"authors\":\"C. E. Gutiérrez\",\"doi\":\"10.1142/9789811222573_0007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Here curlnF(P) is defined as follows. Let P ∈ R3 and n be a unit vector and let S be a surface through P having normal n at P. Consider a closed curve C contained in S and circulating counterclockwise around the point P, and let A be the area of the portion of surface enclosed by C. Then curlnF(P) is the limit of the ratio between the line integral of F over C over the area of A when C shrinks to P, that is,\",\"PeriodicalId\":114943,\"journal\":{\"name\":\"Basic Insights in Vector Calculus\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Basic Insights in Vector Calculus\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789811222573_0007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Basic Insights in Vector Calculus","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789811222573_0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
这里，curlnF(P)的定义如下:让P∈R3和n是一个单位向量,让年代是一个表面通过P正常n P .考虑一个闭合曲线C包含在点P, S和循环逆时针,让一个被包围的部分表面的面积C .然后curlnF之间的比率(P)限制F的线积分/ C / C P,收缩时的面积,
Here curlnF(P) is defined as follows. Let P ∈ R3 and n be a unit vector and let S be a surface through P having normal n at P. Consider a closed curve C contained in S and circulating counterclockwise around the point P, and let A be the area of the portion of surface enclosed by C. Then curlnF(P) is the limit of the ratio between the line integral of F over C over the area of A when C shrinks to P, that is,
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