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I'm interested in finding a free online textbook that is an introductory textbook on numerical PDE for engineers. It should cover the basics of finite differences, finite elements, and Fourier series methods for very simple PDE cases, mainly the 1D heat and 1D wave equations, and should not be concerned with rigor, proofs of convergence, etc.

The purpose of this request is to find a decent online resource for students to use as an alternative to an official course textbook. The students are undergraduate engineers who have seen multivariate calculus and linear algebra but no other mathematics.

Does anybody have suggestions?

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    $\begingroup$ you can certainly do worse than choosing Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations by Lloyd Trefethen. The book (1) covers pretty much all the topics you listed above and (2) is free and available for download here. $\endgroup$ – GoHokies Dec 11 '17 at 19:37
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    $\begingroup$ as a sidenote, there is another free book by the same author covering ODEs, but it relies heavily on MATLAB (and the latter is, unfortunately, not free). $\endgroup$ – GoHokies Dec 11 '17 at 19:40
  • $\begingroup$ @GoHokies Thank you for the suggestion. Trefethen's book is unfortunately too advanced for the intended audience. The students will be undergraduate engineers that only know the basics of multivariate calculus and linear algebra (and nobody masters these subjects after just one semester). $\endgroup$ – Christopher A. Wong Dec 11 '17 at 20:18
  • $\begingroup$ The suggestion by @GoHokies seems reasonable to me. You could just skip the rigorous parts and focus on the methods. Just for curiosity, are you looking something similar to 12 steps to Navier-Stokes $\endgroup$ – nicoguaro Dec 11 '17 at 21:12
  • $\begingroup$ @nicoguaro I briefly looked at the Python notebooks in your link and I would say yes, something like that except for FEM and spectral methods for 1D heat and wave. The issue with Trefethen's book is that a student who has just recently been introduced to a topic cannot "just skip" certain parts because they do not know enough to recognize what to skip and what not to. $\endgroup$ – Christopher A. Wong Dec 11 '17 at 22:15

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