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I am in graduate school for chemical engineering and the method of characteristics appears in many journal articles. Does anyone have a good reference: either online or a book that provides a good explanation with examples of the method of characteristics.

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The journal articles you speak of give no references themselves? – J. M. Dec 15 '10 at 0:58
Method of characteristics should be common enough that one shouldn't have to give references to it when dealing with PDEs. – Willie Wong Dec 15 '10 at 15:10
@Willie: Knowing the chemical engineering literature, they point to a handbook or textbook even if they're using something as simple as Newton-Raphson or Simpson's rule, so I'd think a paper would point to a proper textbook at the very least. – J. M. Dec 15 '10 at 16:17
@J.M.: for some reason you just reminded me of this :) I'll defer to our expertise in this case. – Willie Wong Dec 15 '10 at 22:23
up vote 3 down vote accepted

Off the top of my head, I've found both of these to be well-written and easy to follow. Cavet: I don't have them in front of me, so my recommendation is based on general impressions rather than their particular treatment of characteristics.

  • Partial Differential Equations, by L. C. Evans. Aimed at the intro grad level.
  • Partial Differential Equations, by Walter Strauss. Aimed at an advanced undergrad audience, but good for someone new to the field.

The External Links listed at the end of the wikipedia article on characteristics also look like they might be worth your time.

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Evans's method of characteristics is good for the second time you've seen it. I like Fritz John's PDE for the first time. Same basic feel in both books. – Jack Schmidt Dec 15 '10 at 4:44

Since you have more of an engineering background, I would suggest the textbook of Robert McOwen, Partial Differential Equations: Methods and Applications. Chapter 1 is about solving first order partial differential equations, where the method of characteristics is most applicable. Chapters 2 and 3 also contains some application of the notion of characteristics to higher order equations and to the wave equation.

Compare to the treatments in other standard, more theory-oriented textbooks, I find McOwen's treatment of the method of characteristics to be more detailed and complete, and easier to teach from. As a remark: section 1.3, the application to fully non-linear first order equations, is very difficult to wrap your head around. So don't worry if you feel like you suddenly hit a wall when you get to that section.

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