Mathematics is an important tool to dealing with a complex problem, but it might be too abstract and elusive to be directly applied by engineers. This paper shows mathematics should be simple but effective for thermodynamic problems, the simpler is the better. The two-scale fractal is used as an example to show the im-portance of application of mathematics to practical problems, and a fast-slow law is suggested to deal with many discontinuous problems by fractal calculus.
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