jtbell said:That looks like a major stretch (to put it mildly) for the vast majority of high-school students in the USA, and even for the vast majority of undergraduate university students.
The main focus of "Foundations of Mechanics" is to provide a rigorous and comprehensive treatment of classical mechanics, emphasizing the geometric and variational aspects of the subject. It covers topics such as Newtonian mechanics, Lagrangian and Hamiltonian formalism, and symplectic geometry.
A strong foundation in calculus, linear algebra, and differential equations is necessary to fully comprehend the material in "Foundations of Mechanics." Some knowledge of advanced topics such as differential geometry and functional analysis may also be helpful.
Yes, the theories presented in "Foundations of Mechanics" have many applications in physics, engineering, and other areas of science. For example, Hamiltonian mechanics is commonly used in the study of celestial mechanics and quantum mechanics.
One key difference is the emphasis on geometric and variational aspects of classical mechanics, rather than a purely analytical approach. Additionally, the book covers topics such as Noether's theorem and symplectic geometry in more depth than many other textbooks.
This book can be used for both self-study and in a classroom setting. However, due to its advanced level and mathematical rigor, it may be more beneficial for students to have some guidance from a professor or tutor while studying from this book.