{"title":"Mathematical Proofs","authors":"","doi":"10.1090/mmono/140/08","DOIUrl":"https://doi.org/10.1090/mmono/140/08","url":null,"abstract":"","PeriodicalId":222708,"journal":{"name":"Mathemagics: A Magical Journey Through Advanced Mathematics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114206760","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 : 2020-05-18DOI: 10.1142/9789811214516_0013
{"title":"Answers and/or Hints for Some Odd-Numbered Questions","authors":"","doi":"10.1142/9789811214516_0013","DOIUrl":"https://doi.org/10.1142/9789811214516_0013","url":null,"abstract":"","PeriodicalId":222708,"journal":{"name":"Mathemagics: A Magical Journey Through Advanced Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114099186","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}
3. Since Lp and Lr are subspaces of CX , their intersection is a vector space. It is clear that ‖ · ‖ is a norm (this follows directly from the fact that ‖ · ‖p and ‖ · ‖r are norms). Let 〈fn〉n=1 be a Cauchy sequence in Lp ∩ Lr. Since ‖fm − fn‖p ≤ ‖fm − fn‖ and ‖fm − fn‖r ≤ ‖fm − fn‖ for all m,n ∈ N, it is clear that 〈fn〉n=1 is a Cauchy sequence in both Lp and Lr. Let gp ∈ Lp and gr ∈ Lr be the respective limits of this sequence. Given ε ∈ (0,∞), there exists N ∈ N such that ‖fn − gp‖p < ε(p+1)/p for all n ∈ N with n ≥ N. If n ∈ N and n ≥ N
{"title":"Real Analysis","authors":"Prelim Workshop, Uc Berkeley","doi":"10.2307/j.ctt130hk3w.9","DOIUrl":"https://doi.org/10.2307/j.ctt130hk3w.9","url":null,"abstract":"3. Since Lp and Lr are subspaces of CX , their intersection is a vector space. It is clear that ‖ · ‖ is a norm (this follows directly from the fact that ‖ · ‖p and ‖ · ‖r are norms). Let 〈fn〉n=1 be a Cauchy sequence in Lp ∩ Lr. Since ‖fm − fn‖p ≤ ‖fm − fn‖ and ‖fm − fn‖r ≤ ‖fm − fn‖ for all m,n ∈ N, it is clear that 〈fn〉n=1 is a Cauchy sequence in both Lp and Lr. Let gp ∈ Lp and gr ∈ Lr be the respective limits of this sequence. Given ε ∈ (0,∞), there exists N ∈ N such that ‖fn − gp‖p < ε(p+1)/p for all n ∈ N with n ≥ N. If n ∈ N and n ≥ N","PeriodicalId":222708,"journal":{"name":"Mathemagics: A Magical Journey Through Advanced Mathematics","volume":"41 37","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141204673","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 : 2020-05-18DOI: 10.1142/9789811214516_0012
{"title":"History of Math","authors":"","doi":"10.1142/9789811214516_0012","DOIUrl":"https://doi.org/10.1142/9789811214516_0012","url":null,"abstract":"","PeriodicalId":222708,"journal":{"name":"Mathemagics: A Magical Journey Through Advanced Mathematics","volume":"24 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131840639","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 : 2020-05-18DOI: 10.1142/9789811214516_fmatter
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789811214516_fmatter","DOIUrl":"https://doi.org/10.1142/9789811214516_fmatter","url":null,"abstract":"","PeriodicalId":222708,"journal":{"name":"Mathemagics: A Magical Journey Through Advanced Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117117589","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 : 2020-05-18DOI: 10.1142/9789811214516_bmatter
{"title":"BACK MATTER","authors":"","doi":"10.1142/9789811214516_bmatter","DOIUrl":"https://doi.org/10.1142/9789811214516_bmatter","url":null,"abstract":"","PeriodicalId":222708,"journal":{"name":"Mathemagics: A Magical Journey Through Advanced Mathematics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115309785","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 : 1973-09-30DOI: 10.1142/9789811214516_0011
R. Téman
Calculus: Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems; Riemann integration, Improper integrals; Functions of two or three variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications; Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.
{"title":"Numerical Analysis","authors":"R. Téman","doi":"10.1142/9789811214516_0011","DOIUrl":"https://doi.org/10.1142/9789811214516_0011","url":null,"abstract":"Calculus: Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems; Riemann integration, Improper integrals; Functions of two or three variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications; Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.","PeriodicalId":222708,"journal":{"name":"Mathemagics: A Magical Journey Through Advanced Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120945711","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：