Analysis for Understanding PDEs in Introduction & Farlow Books

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The discussion centers on the upcoming lectures focused on analysis to better understand partial differential equations (PDEs), specifically following the derivation of the heat equation. The student expresses concern about their lack of a strong analysis background and seeks guidance on how in-depth the analysis will go, indicating a desire to prepare in advance. The course utilizes two key textbooks: "Introduction to Partial Differential Equations with Applications" by E. C. Zachmanoglou and Dale Thoe, and "Partial Differential Equations for Scientists and Engineers" by Stanley Farlow. The conversation highlights the importance of real and complex analysis in relation to Fourier Series, including topics such as Fourier Integrals, Dirichlet Kernel, and convergence issues, which are crucial for understanding PDEs.
romsofia
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Hey there, today my prof. said the next two lectures will be completely devoted to analysis in order to understand the PDE's we will be working with (We already derived the heat eq'n). We started off with sets today, not to bad; however, I was wondering how deep will we be going into analysis in order to understand the PDE's, so I could look up stuff (Seems like I'm the only student in the class without a heavy analysis background :X)?

We are using the book "Introduction to Partial Differential Equations with Applications by E. C. Zachmanoglou and Dale Thoe" and "Partial Differential Equations for Scientists and Engineers by Stanley Farlow".

Thanks for any help!
 
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Since we cannot see your profs lesson plans there is no way to answer. Ask your prof.
 
romsofia said:
Hey there, today my prof. said the next two lectures will be completely devoted to analysis in order to understand the PDE's we will be working with (We already derived the heat eq'n). We started off with sets today, not to bad; however, I was wondering how deep will we be going into analysis in order to understand the PDE's, so I could look up stuff (Seems like I'm the only student in the class without a heavy analysis background :X)?

We are using the book "Introduction to Partial Differential Equations with Applications by E. C. Zachmanoglou and Dale Thoe" and "Partial Differential Equations for Scientists and Engineers by Stanley Farlow".

Thanks for any help!

Most of the real and complex analysis in PDE's is related to the Fourier Series, derivation of the Fourier Integrals, Dirichlet Kernel, Parseval's theroem, convergence and divergence of the sereis:

http://en.wikipedia.org/wiki/Fourier_series
 
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