I am soon attending a undergrad course named differential equations and modeling. I have dealt with differential equations before, but in that course just learned a bunch of methods for solving them. Is there any cool books with more 'modeling' view of this subject? Like given a problem A, you have to derive equations for solving it, then solve it. This is often a hard part in math problems in my view.
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One of the best modeling oriented introductions to the study of differential equations is Differential Equations and Their Applications:An Introduction to Applied Mathematics by Martin Braun. It contains not only literally hundreds of detailed models of physical and social phenomena by both ordinary and partial differential equations, it also contains a self-contained introduction to linear algebra and many examples of quantitative analysis of the models via C and Fortran programs.The programming aspects are quite dated now,but they're all easily adapted to modern computer algebra programs like Mathematica or Maple. If you're interested in the theory of differential equations from the modeling perspective, this is where you should start.
Note: this list is different if you meant partial differential equations.