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I would like to get into a career that uses alot of applied math. I took a numerical analysis course in undergrad and liked it, so I plan to self-learn numerical methods for PDEs. Other than the MIT OCW, are there any good textbooks or lectures notes that can be viewed online? Particularly those that are geared towards engineers/scientists, since I'm not into theorems/proofs

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    $\begingroup$ Honestly, I can hardly imagine a guy ponders on numerical methods of PDE, but does not have a stomach for theorems/proofs. What are you preparing to do? eh...... $\endgroup$ – Troy Woo Aug 18 '14 at 17:59
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    $\begingroup$ I think you may have some trouble with numerical PDEs without proofs, because there is more subtlety in numerical PDEs than there is in numerical ODEs. With numerical PDEs, you have to worry about balancing time and space steps to maintain stability; you have to worry about performing your discretization in such a way that you retain conservation laws; you have to know a variety of analytical techniques (for example, weak solutions) to be able to set up the problem; you have to know when to expect seemingly unusual behavior like shocks. $\endgroup$ – Ian Aug 18 '14 at 18:00
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If you want to do applied math without theory, then respectfully, you shouldn't go into applied math. Even applied mathematicians care about where things come from and how to justify them, so you won't be able to avoid proofs and theorems.

With that said, a few of my favorite resources are as follows:

  1. Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque
  2. Numerical Methods for Conservation Laws by Randall J. LeVeque
  3. A Friendly Introduction to Numerical Analysis by Brian Bradie
  4. Elementary Applied Partial Differential Equations by Richard Haberman

Randall LeVeque is awesome in general. He also developed some pretty cool PDEs software to go along with his books.

An essential PDEs source would be Partial Differential Equations by Lawrence Evans. That one is all theory, but it's all necessary for developing numerical PDEs methods.

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  • $\begingroup$ What is the difference between the two books by LeVeque? You need to read the first one in order to understand the second one? (Asking mainly because the second one has a very good price. $\endgroup$ – David Mar 22 at 22:42
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    $\begingroup$ The second treats a particular type of PDE; the first is a bit more comprehensive, but less in-depth. $\endgroup$ – artificial_moonlet Mar 24 at 18:44

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