Learning Intro PDE: Farlow vs Hillen vs Pinsky

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Discussion Overview

The discussion revolves around recommendations for introductory textbooks on partial differential equations (PDEs), particularly in the context of a math undergraduate course. Participants compare different books, their approaches, and their suitability for various academic focuses, including applications and physical interpretations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant mentions using Farlow's PDE book, noting its solid content but also the divergence in methods from their professor.
  • Another participant suggests that recommendations may vary depending on whether the course is for a physics, math, or engineering major.
  • A different participant recommends Asmar's book for its application-focused approach, stating it serves well for solving PDEs with some theoretical motivation.
  • One participant describes Farlow's book as intuitive and relaxed compared to others that are more theory-heavy, suggesting that books focused on mathematical methods for physics or engineering might be more aligned with Farlow's style.
  • Links to additional resources, such as a free book by Nearing, are provided as potential alternatives for further exploration.

Areas of Agreement / Disagreement

Participants express differing opinions on the best introductory PDE textbooks, with no consensus on a single recommended book. Various perspectives highlight the importance of application versus theory in the choice of textbooks.

Contextual Notes

Some participants note the importance of matching textbook recommendations to the specific academic focus of the course, indicating that different majors may benefit from different approaches to PDEs.

Who May Find This Useful

Math undergraduates, educators seeking textbook recommendations for PDE courses, and individuals interested in the application of PDEs in physics and engineering contexts.

LoganS
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So I am currently a math undergraduate (senior though) taking an introduction partial differential equations. We are using the PDE book by Farlow (Dover reprint). It seems to be a solid book though my professor does diverge from the methods used in it fairly regularly (like not making assumptions they do, utilizing newer techniques, and small stuff like different notation).

I was wondering if anybody here had a recommendation on what another good intro book would be? I mainly want something that has more examples and problems to work, and a good explanation with respect to physical interpretation.

Two books I found are:
1) Partial Differential Equations: Theory and Completely Solved Problems by Hillen et al.
Pro: From the pages you are shown on Amazon they seem to utilize identical methods and notation as my class does.

2) Partial Differential Equations and Boundary-value Problems With Applications by Pinsky
Pro: I used a book from the same series for my intro to real analysis, and I liked it.

Any recommendations or comments would be appreciated.
 
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Are you taking this course for physics major or math major or engineer major?

Cause accordingly the suggestions will be offered.
 
I am a math major. Sorry about that I'll edit the post to include it.
 
I used Partial Differential Equations with Fourier Series and Boundary Value Problems by Asmar. I liked it for a first course in PDE. Heavily focused on application side with some theory thrown in and if all you're looking for is method for solving some PDE with some motivation it served its purpose rather well.
 
Farlow is the most intuitive and relaxed PDE book I am aware of. Most books have much more theory, proofs, discussions of Sturm-Liouville theory, etc. So if you are looking for a few examples along the lines of Farlow perhaps math methods for physics / engineering type books may be the place to look. Check your library for titles like, "advanced engineering math" or "math methods for physicists". One example is the very good (and free!) book by Nearing:

http://www.physics.miami.edu/~nearing/mathmethods/

jason
 

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