Pub Date : 1900-01-01DOI: 10.1109/9780470546765.ch35
J. Vince
Just as derivatives can be used to explore the properties of functions of 1 variable, so also derivatives can be used to explore functions of 2 variables. In this section, we begin that exploration by introducing the concept of a partial derivative of a function of 2 variables. In particular, we de ne the partial derivative of f (x; y) with respect to x to be fx (x; y) = lim h!0 f (x+ h; y) f (x; y) h when the limit exists. That is, we compute the derivative of f (x; y) as if x is the variable and all other variables are held constant. To facilitate the computation of partial derivatives, we de ne the operator
正如导数可以用来研究一元函数的性质一样，导数也可以用来研究二元函数。在本节中，我们通过引入两个变量函数的偏导数的概念开始探索。特别地，我们求出f (x)的偏导数 ;Y)关于x等于fx (x;Y) = lim h!0 f (x+ h;Y) f (x;Y) h，当极限存在时。也就是说，我们计算f (x)的导数;Y)，就好像x是变量，而所有其他变量都保持不变。为了方便偏导数的计算，我们引入了 算子
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Pub Date : 1900-01-01DOI: 10.1007/978-1-4471-5466-2_4
J. Vince
{"title":"Derivatives and Antiderivatives","authors":"J. Vince","doi":"10.1007/978-1-4471-5466-2_4","DOIUrl":"https://doi.org/10.1007/978-1-4471-5466-2_4","url":null,"abstract":"","PeriodicalId":143920,"journal":{"name":"Calculus for Computer Graphics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129786697","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}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-11376-6_9
J. Vince
{"title":"Arc Length and Parameterisation of Curves","authors":"J. Vince","doi":"10.1007/978-3-030-11376-6_9","DOIUrl":"https://doi.org/10.1007/978-3-030-11376-6_9","url":null,"abstract":"","PeriodicalId":143920,"journal":{"name":"Calculus for Computer Graphics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129107624","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}
Pub Date : 1900-01-01DOI: 10.1007/978-3-031-28117-4
J. Vince
{"title":"Calculus for Computer Graphics","authors":"J. Vince","doi":"10.1007/978-3-031-28117-4","DOIUrl":"https://doi.org/10.1007/978-3-031-28117-4","url":null,"abstract":"","PeriodicalId":143920,"journal":{"name":"Calculus for Computer Graphics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131460768","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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