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Physics from a Mathematical Point of View: Mathematical Methods of Classical Mechanics
This is a very good book, which can be regarded as a mathematical expression of classical mechanics. Before considering the mathematical problems of physics, it is reflected here.

Physics seems to be simpler than mathematics, but it is only a superficial impression. Physics involves a wide range of mathematical theories. These theories are manifested in various solutions, such as solving equations of motion, that is, using differential equations. When solving the motion equation of a simple pendulum, we get an inaccurate but practical formula through linear approximation.

There are many kinds of calculus. Displacement is the integral of velocity, and velocity is the derivative of displacement. These basic mathematical methods are still easy to identify. But when it comes to the conservation of system energy, the situation is complicated. By introducing symmetry, all possible motions that keep the energy of the system constant can form a motion group, which involves group theory, which is still relatively abstract. In addition, considering principle of least action, the motion of the system is always a minimal curve in the phase space of the system, which involves the contents of differential geometry and functional analysis. When it comes to quantum mechanics and statistical mechanics, we have to face more abstract Hilbert space, probability statistics, stochastic processes and other more complex mathematics.

Fortunately, the mathematics used in physics is ordinary, because the real world can always be regarded as continuous or even infinitely differentiable, and the influence of various high-order terms can also be ignored through the linear approximation of Taylor formula. Although this is by no means the case, the development of physical theory needs to consider the main factors, not all factors. This is why although many basic mathematical problems are still being studied, physics can go beyond the limitations of mathematics and obtain unreliable but feasible methods.

Calculus, variational function and generalized function are all born from physics first and then refined by mathematicians.

I have read several pages of this book before. If I am interested in it, it is a very good book. The correspondence between various mathematical objects and physical objects is very smooth, which can make mathematics come out of textbooks and draft papers and apply it to the vast real world. Learning is no longer useless.

But if the foundation is poor and the understanding of various mathematical concepts is not thorough, this book will become a boring math book, so it is better to put it down first. If you don't have enough skills, it is easy to understand the deviation and choose according to your own conditions.