This is the first in a series of four volumes, all written at an elementary calculus level. The complete course covers the most important areas of classical physics such as mechanics, thermodynamics, statistical mechanics, electromagnetism, waves, and optics. The volumes result from a translation, an in depth revision and update of the Italian version published by Decibel-Zanichelli. This first volume deals with classical mechanics, including an introduction to relativity.
The laws of Physics, and more in general of Nature, are written in the language of mathematics. The reader is assumed to know already the basic concepts of
calculus: functions, limits, and the differentiation and integration operations. We
shall however, without mathematical rigor, give the necessary information on
vectors and matrices.
Physics is an experimental science, meaning that it is based on the experimental
method, which was developed by Galileo Galilei in the seventeenth century. He
taught us, in particular, that to try to understand a phenomenon one must simplify as
much as possible the relevant working conditions, understanding which of the
aspects are secondary and eliminating them as far as possible. The understanding
process is not immediate, but rather it proceeds by trial and error, in a series of
experiments, which might lead, with a bit of fortune and a lot of thinking, to
discover the governing laws. Induction of the physics laws process goes back from
the observed effects to their causes, and, as such, cannot be purely logic. Once a
physical law is found, it is necessary to consider all its possible consequences. This
is now a deductive process, which is logical and similar to the mathematical one.
Each of the consequences, the predictions, of the law must then be experimentally
verified. If only one prediction is found to be false by the experiment, even if
thousands of them had been found true, it is enough to prove that the law is false.
This implies that we can never be completely sure that a law is true; indeed the
number of its possible predictions does not have limits, and in any historical
moment not all of them have been controlled. However, this is the price we must
pay in choosing the experimental method, which has allowed humankind to
advance in the past four centuries much more than in all the preceding millennia.