{"title":"Smooth Manifolds with a Connection","authors":"","doi":"10.1002/9781119517566.ch18","DOIUrl":"https://doi.org/10.1002/9781119517566.ch18","url":null,"abstract":"","PeriodicalId":220953,"journal":{"name":"Semi‐Riemannian Geometry","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121891132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Differentiation and Integration on Smooth Manifolds","authors":"","doi":"10.1002/9781119517566.ch16","DOIUrl":"https://doi.org/10.1002/9781119517566.ch16","url":null,"abstract":"","PeriodicalId":220953,"journal":{"name":"Semi‐Riemannian Geometry","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129832567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Applications to Physics","authors":"Liming Pang","doi":"10.1002/9781119517566.ch22","DOIUrl":"https://doi.org/10.1002/9781119517566.ch22","url":null,"abstract":"i.e., Work = Force × Distance. And the unit for work is Joule (denoted by J). 1 J = 1 N × 1 m. But in reality, force is not always constant, but a function in terms of position, say F = f(x). In such circumference, we can also define the work using integration: Divide the interval [a, b] into n pieces of length ∆x = b−a n , and in each interval, we take a point xi ∈ [xi−1, xi]. When ∆x is small, the force is almost constantly equal to f(xi ), so an approximation of the actual work is: n ∑","PeriodicalId":220953,"journal":{"name":"Semi‐Riemannian Geometry","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130996747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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