Until now I had referred to popular science or essays books, but in this post I comment on “No-Nonsense Classical Mechanics” by Jakob Schwichtenberg, which would be more akin to a textbook.

The content of the book is an introduction to the different **formulations **of **Classical Mechanics** – **Newtonian**, **Lagrangian **and **Hamiltonian**, mainly (*) – showing us their mathematical frameworks, their differences and relationships, their motivations and for which systems or situations each one is more appropriate.

*(*) Note: also presents the Koopman-von Neumann formulation, and what he calls ‘alternative methods’ such as the “Statistical” and “Hamilton-Jacobi” ones*

Why do I comment on a book like this? Well, because it’s not a standard work.

As the subtitle indicates, it is a “**student-friendly**” book, a label analogous to “user-friendly” which defines intuitive and easy-to-use computer programs.

It has been elaborated with that design philosophy: the reader has always been taken into account, presenting the material in a very friendly way to facilitate its study and learning.

The book has a clear pedagogical approach (you may ask: what textbook doesn’t have it? Well, I would say more than one, judging by the results).

To develop this idea a little more, I comment some characteristics that I see in the book:

**Exposition and explanations**

The author has taken great care in these facets.

An **accessible language style** with good use of **analogies **to present concepts that may be more abstract or difficult for the student

Doesn’t mind repeatedly stressing the most important issues to emphasize them or those that may be harder to understand to present them with different approaches.

What does this mean?

It’s writing style is neither dry nor extremely concise. Other authors seem to focus only on the most capable students or on showing their mastery of the subject.

In this case, the author strives to help students with the parts he knows from experience will be harder for them. In addition, he captures their attention when he presents the fundamental ideas and tries to leave them anchored in their learning.

Every block have a introductory framework where the topics are contextualized and a final summary that compiles and synthesizes what has been discussed. Both sections are very well written and are very useful for understanding the ideas presented.

It also uses resources that complement this exhibition very well:

- Many
**handmade drawnings**, which make it easier to understand what it explains. **Diagrams**that visually organize the concepts presented.- A lot of
**notes**, included in the**side margins**of the pages, about. mathematical issues or relating ideas. I think it’s a better place than at the end of the book, although some could be part of the main text. - In addition, this page layout leaves space for the reader to write his/her own notes.
- It has some
**appendices**, also ‘student-friendly’, about mathematical methods and tools used in the main content.

**Nothing is taken for granted.**

Any physical concepts mentioned are explained or recalled, especially from a “qualitative” point of view.

The “jumps” in mathematical development are avoided. Many textbooks -wrongly in my view- leave steps unexplained, either because they consider them obvious (even if they are not trivial) or as work for the reader (treating as exercises what should be an explanation).

**Insight**

It provides us with those “eureka moments” where we say: I really understand this at last!

It’s not only a matter of detailing such an equation or deriving a particular application from it – which also – but of understanding why, the motivations for using a particular formulation, where all this comes from and its relations with other areas.

To give a couple of examples (this review wanted to focus on the pedagogical approach of the book rather than on its content itself):

- How it connects the symmetries of a system with the existence of conserved quantities (momentum, energy,…) through Noether’s theorem
- How it shows us the relationships between Classical and Quantum Mechanics and the origin of the Principle of Minimum Action.

**What category would I place this book in and who might be interested?**

In terms of level and style, it could be placed between high quality lecture notes made by an excellent student and a standard university textbook.

For which audience is this book useful and attractive? I see mainly two profiles:

- The student who has this subject in his/her grade and wants an introduction from “zero”, step by step, with a comprehensive treatment, not superficial.

For those who find some difficulty in the bibliography usually recommended in Classical Mechanics (Goldstein, Landau, Morin,…), this book can smooth the way and make it easier to study.

It should also be pointed out that this book doesn’t help them to practice solving problems. Only some basic illustrative examples are included, so they should refer to complementary books and resources. - Advanced amateurs who enjoy learning (or rediscovering, depending on their academic background) about areas of Physics or Science in general.

It’s a work that could somehow fill the gap between popular science books and textbooks (closer to the latter).

For these readers, its very accesible mathematical treatment allows them a deeper understanding of the subject.

**Philosophy of the author of the “No-Nonsense” books**

The author, Jakob Schwichtenberg started with “Physics from Symmetry” (at the moment with free access), a publishing success in its category, and this encouraged him to continue writing.

Apart from other works he has published (check his website), there are also available in this “No-Nonsense” series the titles on **Quantum Mechanics**, **Quantum Field Theory** and **Electrodynamics **that follow the same philosophy as this one.

Both on his web pages and in the introduction to the books, Jakob defines his philosophy in writing them. I encourage you to read his approach: these are ideas that I fully share and he expresses them very well

There are resonances from Feynman and other authors who have already pointed out all these defects in the teaching of physics or any subject that could have a certain complexity. In this sense, I remembered the sentence of the Nobel Prize winner in Physics Luis Walter Álvarez:

“We are in an advanced physics class. This means that the subject is confusing to the instructor. Otherwise, he would call it elementary physics.”

Of course, this doesn’t mean that understanding the ins and outs of the Lagrangian or Hamiltonian formulation of Classical Mechanics or understanding the foundations of Quantum Mechanics -to quote another of his books- is ‘a piece of cake’. You have to work hard on them: study with interest, consult multiple sources, practice solving problems and acquire an adequate mathematical base.

There is no discussion of this, but I don’t think we should complicate this learning any more than necessary with texts that are too intrincate or that obviate many of the difficulties encountered by beginners.

I think that some authors use (nearly) the same style when writing a scientific paper for professionals (where, in any case, clarity is also appreciated) as when writing a pedagogical work aimed at students.

They must be two totally different approaches!

**Other similar books**

I haven’t done an exhaustive search of these kinds of books, but I don’t think there are many.

The most similar precedent (as far as I know) is the series “The Theoretical Minimun” published by the prestigious physicist Leornard Susskind with several collaborators. Its contents comes from his MOOCs (free online courses) and cover the titles of Classical Mechanics, Quantum Mechanics and Special Relativity.

Although “Classical Mechanics (TheTheoretical Minimum)” is a very interesting work (I recommend the whole series), it has a more concise treatment, less rich in explanations and details than the “No-Nonsense”, possibly conditioned by being a “low-cost” edition of smaller format and less extension.

Another great series is “A Student’s Guide” by Cambridge University Press. I quite liked the one dedicated to Maxwell’s Equations and Schrödinger’s Equation (both by Dan Fleisch). They are also introductory and complementary books to the more advanced textbooks, with special care in the explanations of both the mathematics used and the physical concepts.

However, in classical mechanics, although I’ve only read some parts of “A Student’s Guide for the Lagrangians and Hamiltonians” (Patrick Hamill), has seemed to me more like a standard textbook. My first impression (which may be wrong) is that it doesn’t have the same pedagogical quality.

**What did I think of the book?**

It was a book that surprised me and I enjoyed it.

At first, being a textbook format, I only expected to consult some sections to remember or better understand certain ideas, but I found myself reading it completely and in much more detail than I could have imagined.

In fact, it has encouraged me to buy “No-NonSense Quantum Mechanics”, and perhaps I will continue with others of the series.

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