Two general questions about differential equations.

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Discussion Overview

The discussion revolves around the study of ordinary differential equations (ODEs) and partial differential equations (PDEs), focusing on the search for application-oriented resources and the prerequisites necessary for understanding PDEs. Participants share recommendations for books and inquire about the necessary mathematical background.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant expresses a desire for a book focused on the applications of ODEs, seeking resources that emphasize mathematical modeling of physical situations.
  • Another participant suggests 'Differential Equations' by Simmons as a suitable resource, noting its inclusion of physics problems.
  • There is a discussion about the prerequisites for studying PDEs, with one participant stating that familiarity with calculus of several variables and some functional analysis is necessary.
  • A participant questions whether knowledge of multi-variable Real Analysis is required, mentioning their completion of Rudin's mathematical analysis up to Chapter 5 and seeking clarification on further study before tackling PDEs.

Areas of Agreement / Disagreement

Participants generally agree on the importance of certain mathematical prerequisites for understanding PDEs, but there is no consensus on the specific resources or the extent of prior knowledge required.

Contextual Notes

Participants express varying levels of familiarity with mathematical analysis and its relevance to PDEs, indicating potential gaps in assumptions regarding prior knowledge.

AdrianZ
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I'm currently studying ODE's from Boyce's 'Elementary differential equations and Boundary value problems', It's a good book and it also explains some physical applications of differential equations, but I'm looking for a book that its main topic is about how to write differential equations for various mathematical modelings of physical situations. I'd like to know more about ' the applications of ODE's ' and I'm looking for a book that is more application oriented.

my next question is what prerequisites I need to know before I can understand a book about PDE's.

Thanks in advance.
 
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No ideas?
 
Have you tried 'Differential Equations' by Simmons? It's a good book & contains many problems in physics.
For a course in PDEs, you must be familiar with calculus of several variables & a little functional analysis.
 
Eynstone said:
Have you tried 'Differential Equations' by Simmons? It's a good book & contains many problems in physics.
For a course in PDEs, you must be familiar with calculus of several variables & a little functional analysis.

Do you mean "Differential equations (with applications and historical notes)" by George f. Simmons published by McGraw-Hill?

Do I need to know multi-variable Real Analysis? I mean I've already read Rudin's mathematical analysis to the end of Chapter 5. am I prepared or I need to study next chapters too before I can understand PDE's?
 

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