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Since materials modelling is made possible primarily because of the availability of mathematical models, are there any resources that provide a mathematics heavy picture of materials behaviour?

I am interesting in finding out if there are any courses or textbooks that have incorporated mathematics and simple computational modelling as a part of introducing concepts from areas like physical metallurgy, materials thermodynamics, environmental degradation of materials, solid state physics etc. at the undergraduate level.

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I think that material modeling is made possible primarily due to physical models instead of mathematical/computational ones. A mathematical/computational model, per se, don't have any information/interpretation about the system.

Once the physics behind the process/phenomenon is understood, it is modeled using tools like mathematics, as needed.

Normally, in the Physics courses are disciplines dedicate to the mathematical tools useful in Physics called Mathematical Physics. In the Google Books resource you can find many books with this subject, for example.

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    $\begingroup$ I do agree that understanding the physics enables mathematical modelling. However, the spirit of the question here is to find out if there are any resources that collectively teach materials science subjects by adopting such an approach. Materials Science and Engineering is a department on its own with its own curriculum in many universities, so redirecting to Mathematical Physics (which is the superset) seems a little unfair. $\endgroup$
    – Mythreyi
    May 15, 2020 at 19:30
  • $\begingroup$ The problem is that the mathematical methods are common between different Material Science and Engineering courses (also as in Solid State Physics, Semiconductor Physics, etc.), so, it is more efficient (from the didactic, teaching and student point of views) to have a general course in Mathematical Physics than repeating part of the same content in several disciplines. As a professor that lectutred both type of courses, is easier that the person has previous knowledge about Mathematical Physic and then "adapt" them to the specifications of the individual areas. $\endgroup$
    – Camps ♦
    May 15, 2020 at 19:42
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    $\begingroup$ Exactly! Previous knowledge is important and definitely helps in application to different cases. What I am curious to know is if there are such adaptations available as resources. $\endgroup$
    – Mythreyi
    May 15, 2020 at 19:57
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    $\begingroup$ I don't have any experience with teaching courses, but I have personally benefitted by taking courses that teach a core concept in different flavours (eg: numerical methods from the mathematics department and a similar course from the physics department). So, I don't fully agree that there should be only general courses. $\endgroup$
    – Mythreyi
    May 15, 2020 at 19:58

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