Dimensional analysis, one of the topics in the book, is a favorite of mine. Unfortunately the more useful parts of the subject are not that well known. Fortunately, this book seems to have a fairly standard introduction to the subject.
Most people seem to think dimensional analysis is limited to checking that the dimensions are consistent ("dimensional homogeneity"). But dimensional homogeneity is a constraint which can simplify problems, sometimes even allowing them to be solved up to a constant. The latter often requires additional reasoning to determine which variables are relevant and which are not. Kolmogorov famously made use of this approach to obtain his "5/3" law in turbulence: https://micromath.wordpress.com/2008/04/04/kolmogorovs-53-la...
The details of dimensional analysis seem only to be taught to engineers taking fluid dynamics or heat transfer classes. I understand why: the Navier-Stokes equations for fluid motion typically can't be solved in practice (for the most part), but we usually know which quantities are involved because they appear in the Navier-Stokes equations. Then it's useful to use that as a basis for analysis. In other areas, you can usually solve the equations, so dimensional analysis may not be necessary. Add on top of that the use of physical models (not mathematical or computational models), which may be scale models like a small scale airplane in a wind tunnel. Dimensional analysis provides a basis for scaling.
I'd recommend reading the relevant chapter of the book if you're interested. Dimensional analysis is most useful for physical problems, but you sometimes can generalize the idea of a "dimension" such that two things have different dimensions when it does not make sense to add them.
Most people seem to think dimensional analysis is limited to checking that the dimensions are consistent ("dimensional homogeneity"). But dimensional homogeneity is a constraint which can simplify problems, sometimes even allowing them to be solved up to a constant. The latter often requires additional reasoning to determine which variables are relevant and which are not. Kolmogorov famously made use of this approach to obtain his "5/3" law in turbulence: https://micromath.wordpress.com/2008/04/04/kolmogorovs-53-la...
The details of dimensional analysis seem only to be taught to engineers taking fluid dynamics or heat transfer classes. I understand why: the Navier-Stokes equations for fluid motion typically can't be solved in practice (for the most part), but we usually know which quantities are involved because they appear in the Navier-Stokes equations. Then it's useful to use that as a basis for analysis. In other areas, you can usually solve the equations, so dimensional analysis may not be necessary. Add on top of that the use of physical models (not mathematical or computational models), which may be scale models like a small scale airplane in a wind tunnel. Dimensional analysis provides a basis for scaling.
I'd recommend reading the relevant chapter of the book if you're interested. Dimensional analysis is most useful for physical problems, but you sometimes can generalize the idea of a "dimension" such that two things have different dimensions when it does not make sense to add them.