Pub Date : 2018-07-03DOI: 10.1142/9789813270886_0010
{"title":"PDEs with Self-Adjoint Operators","authors":"","doi":"10.1142/9789813270886_0010","DOIUrl":"https://doi.org/10.1142/9789813270886_0010","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130611218","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 : 2018-07-03DOI: 10.1142/9789813270886_fmatter
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789813270886_fmatter","DOIUrl":"https://doi.org/10.1142/9789813270886_fmatter","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114284370","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 : 2018-07-03DOI: 10.1142/9789813270886_0012
{"title":"Similarity Transformations","authors":"","doi":"10.1142/9789813270886_0012","DOIUrl":"https://doi.org/10.1142/9789813270886_0012","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131364721","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 : 2018-07-03DOI: 10.1142/9789813270886_0011
C. E. Gutiérrez
1. Systems of 1st order ordinary differential equations 2 1.1. Existence of solutions 2 1.2. Uniqueness 4 1.3. Differentiability of solutions with respect to a parameter 6 2. Quasi-linear pdes 10 2.1. Step 1 10 2.2. Step 2 11 2.3. Cauchy problem 11 3. Degenerate case 12 4. Examples 14 4.1. Example 1 14 4.2. Example 2 14 4.3. Example 3 14 4.4. A maximum principle for a first order pde 15 5. Fully nonlinear case 15 5.1. Cauchy problem 17 5.2. Uniqueness 21 5.3. Solution of the eikonal equation 22 5.4. Higher dimensional case 23 6. A transversality problem 24 7. The Legendre transform 25 References 27
{"title":"First Order PDEs","authors":"C. E. Gutiérrez","doi":"10.1142/9789813270886_0011","DOIUrl":"https://doi.org/10.1142/9789813270886_0011","url":null,"abstract":"1. Systems of 1st order ordinary differential equations 2 1.1. Existence of solutions 2 1.2. Uniqueness 4 1.3. Differentiability of solutions with respect to a parameter 6 2. Quasi-linear pdes 10 2.1. Step 1 10 2.2. Step 2 11 2.3. Cauchy problem 11 3. Degenerate case 12 4. Examples 14 4.1. Example 1 14 4.2. Example 2 14 4.3. Example 3 14 4.4. A maximum principle for a first order pde 15 5. Fully nonlinear case 15 5.1. Cauchy problem 17 5.2. Uniqueness 21 5.3. Solution of the eikonal equation 22 5.4. Higher dimensional case 23 6. A transversality problem 24 7. The Legendre transform 25 References 27","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116926308","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 : 2018-07-03DOI: 10.1142/9789813270886_bmatter
{"title":"BACK MATTER","authors":"","doi":"10.1142/9789813270886_bmatter","DOIUrl":"https://doi.org/10.1142/9789813270886_bmatter","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133256469","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 : 2018-07-03DOI: 10.1142/9789813270886_0007
M. Tirelli
Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a system of difference equations. In many interesting cases such difference equations are nonlinear; as you will see, even the textbook, deterministic, neoclassical, growth model is represented by a system of nonlinear equations. Although nonlinearities make the study of dynamic economic systems difficult, we can still hope to derive useful characterizations and results. This is achieved either locally, in a neighborhood of an equilibrium point, or globally for log-linearized systems. In both cases, non-linear systems are studied using the theory of linear difference equations. In these notes we shall summarize some useful results in this theory and apply them to deal with dynamic economic systems. In these class notes I present some useful material on how to solve linear difference equations and study solution stability. These notes are incomplete; many important questions are left unexplained; but students can find additional, sharp and clear material in Elaydi (2005) ”An Introduction to Difference Equations”, Springer-Verlag. A general, introductory, reference is Simon & Blume, ”Mathematics for Economists”, Norton. For issues on linear algebra, my favorite textbook is Serge Lang ”Linear Algebra”, Springer-Verlag.
动态经济模型是研究经济动态和更好地理解经济增长和经济周期等相关现象的有用工具。平衡条件通常由一组差分方程和一组边界条件(描述某些变量的极限值)来确定。因此，研究平衡性质需要研究一个差分方程系统的性质。在许多有趣的情况下，这样的差分方程是非线性的;正如你将看到的，即使是教科书上的、确定性的、新古典主义的增长模型，也是由一个非线性方程系统来表示的。尽管非线性使动态经济系统的研究变得困难，我们仍然希望得到有用的表征和结果。对于对数线性化系统，这可以在局部、平衡点的邻域或全局中实现。在这两种情况下，非线性系统都是用线性差分方程理论来研究的。在这些注释中，我们将总结这一理论中的一些有用的结果，并将它们应用于处理动态经济系统。在这些课堂笔记中，我介绍了一些关于如何求解线性差分方程和研究解的稳定性的有用材料。这些笔记是不完整的;许多重要的问题没有得到解释;但学生可以在Elaydi(2005)的《差分方程导论》(Springer-Verlag, An Introduction to Difference Equations)中找到额外的、尖锐而清晰的材料。一个一般的，介绍性的参考资料是西蒙和布卢姆，“经济学家的数学”，诺顿。关于线性代数的问题，我最喜欢的教科书是Serge Lang的《线性代数》，Springer-Verlag。
{"title":"Linear Difference Equations","authors":"M. Tirelli","doi":"10.1142/9789813270886_0007","DOIUrl":"https://doi.org/10.1142/9789813270886_0007","url":null,"abstract":"Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a system of difference equations. In many interesting cases such difference equations are nonlinear; as you will see, even the textbook, deterministic, neoclassical, growth model is represented by a system of nonlinear equations. Although nonlinearities make the study of dynamic economic systems difficult, we can still hope to derive useful characterizations and results. This is achieved either locally, in a neighborhood of an equilibrium point, or globally for log-linearized systems. In both cases, non-linear systems are studied using the theory of linear difference equations. In these notes we shall summarize some useful results in this theory and apply them to deal with dynamic economic systems. In these class notes I present some useful material on how to solve linear difference equations and study solution stability. These notes are incomplete; many important questions are left unexplained; but students can find additional, sharp and clear material in Elaydi (2005) ”An Introduction to Difference Equations”, Springer-Verlag. A general, introductory, reference is Simon & Blume, ”Mathematics for Economists”, Norton. For issues on linear algebra, my favorite textbook is Serge Lang ”Linear Algebra”, Springer-Verlag.","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126741150","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 : 2018-07-03DOI: 10.1017/cbo9781107279124.004
A. Rasmuson, B. Andersson, L. Olsson, Ronnie Andersson
{"title":"Model Formulation","authors":"A. Rasmuson, B. Andersson, L. Olsson, Ronnie Andersson","doi":"10.1017/cbo9781107279124.004","DOIUrl":"https://doi.org/10.1017/cbo9781107279124.004","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132313779","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 : 2018-07-03DOI: 10.1142/9789813270886_0014
{"title":"Appendix","authors":"","doi":"10.1142/9789813270886_0014","DOIUrl":"https://doi.org/10.1142/9789813270886_0014","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122648839","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 : 2018-07-03DOI: 10.1142/9789813270886_0002
{"title":"Model Simplifications and Approximations","authors":"","doi":"10.1142/9789813270886_0002","DOIUrl":"https://doi.org/10.1142/9789813270886_0002","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134374891","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 : 2018-07-03DOI: 10.1142/9789813270886_0003
{"title":"Examining a Model","authors":"","doi":"10.1142/9789813270886_0003","DOIUrl":"https://doi.org/10.1142/9789813270886_0003","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133233028","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：