{"title":"DIFFERENTIAL EQUATIONS","authors":"Hengtai Wang, Aminu Ma, aruf Nass, Zhiwei Zou","doi":"10.1201/9781315275451-15","DOIUrl":"https://doi.org/10.1201/9781315275451-15","url":null,"abstract":"In the last century, fractional partial differential equations (FPDEs) have played important rules in the fields of science and engineering, for instance, physics, chemistry, biology, andcontrol theory. Recently, those class of differential equations has also attracted much more interest of mathematicians and physicists [1–6]. Finding the best methods of obtaining the exact solutions of differential equations remains one of the unanswered questions in the field. Many approaches have been developed by mathematicians to study the solutions of PFDEs, such as Adomian decomposition method, the fractional subequation method, numerical method, the first integral method, and Lie symmetry method [7–14]. In this article, we consider one of the powerful techniques of solving and analyzing differential equations, i.e., the Lie symmetry method. The Lie symmetry method is widely used to transformed partial differential equations (PDEs) into ordinary differential equations (ODEs), and the ODE is later solve numerically or analytically using similarity invariant [7, 9, 10, 12, 14–22]. Lie symmetry is also utilized in obtaining the conservation laws (Cls) [23]. The method developed by Noether theorem [24] and Ibraginov’s [25] is one of the best and simplest methods of evaluating Cls of differential equations. Consider general forms of fractional differential equations:","PeriodicalId":129704,"journal":{"name":"Matrix Algebra Using MINimal MATlab","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126784102","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":"WARMUP","authors":"Toke Eskildsen","doi":"10.1201/9781315275451-7","DOIUrl":"https://doi.org/10.1201/9781315275451-7","url":null,"abstract":"In all homework assignments and projects, you will be writing Java code to write a program (or applet) according to the specification given in the assignment. Your program must meet all the requirements described in the assignment, but you are welcome to add extra features and embellish on the description here. Always check the syllabus page for a link to a page with demos of the assignments; most assignments will have these demos available.","PeriodicalId":129704,"journal":{"name":"Matrix Algebra Using MINimal MATlab","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116624557","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":"JORDAN NORMAL FORM","authors":"K. Kamdin","doi":"10.1201/9781315275451-20","DOIUrl":"https://doi.org/10.1201/9781315275451-20","url":null,"abstract":"This paper outlines a proof of the Jordan Normal Form Theorem. First we show that a complex, finite dimensional vector space can be decomposed into a direct sum of invariant subspaces. Then, using induction, we show the Jordan Normal Form is represented by several cyclic, nilpotent matrices each plus an eigenvalue times the identity matrix – these are the Jordan","PeriodicalId":129704,"journal":{"name":"Matrix Algebra Using MINimal MATlab","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125524294","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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