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Uno degli ultimi libri di Bruno Latour, una curatela che articola la sua proposta di una nuova cosmologia basata sulle scienze della Terra, un nuovo modo di intendere la nostra vita sullo spazio finito della Terra.

juancarlos DOT demartin AT polito DOT it

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This is the newest edition of George F. Simmons’s famous “Differential Equations with Applications and Historical Notes.” t drastically changed my outlook on a large part of mathematics. For example, we might wonder why do we put so much effort in studying the convergence of power series in analysis II? The subject is interesting on its own, but aside from the abstract interest, it’s ultimately because we want to use those methods to understand power series solutions of differential equations.
This book is clearly written, and it not only makes the subject interesting but deeply fascinating. Great mathematicians like Gauss and Laplace were trying to solve problems of physics and engineering, in which differential equations are ubiquitous, and these problems are the primary motivation for a large part of analysis and topology. Unlike other books on ODE, Simmons’ exercises are fun. It was fun just to read them, and each one got me excited to try to find out the answer.

I am aware that the university library has the first edition copy (1972), but this latest 3rd edition was augmented with a chapter dedicated to Laplace transform, improvements on the explanations of Abel’s mechanical problem, tautochrone, Van der Pol equations (Nonlinear dynamics-discussed in classical mechanics courses), and etc.

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This is not a typical advanced calculus book. This was written by one of the greatest mathematicians of our era, Terence Tao. He actually wrote two books for undergraduate students, “Analysis I” and “Analysis II.” In this book, he discusses topics like metric spaces, uniform convergence, Lebesgue measures, and Lebesgue integration. These topics are not very well discussed in a typical advanced calculus book (or Analysis II or Analysis I). What’s more surprising is that despite the difficulty of the topics he discusses, Tao made the book quite readable; it can be casually read and understood without picking up a pencil during reading.

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Since the 1950s, this has been the acknowledged standard in advanced (graduate or advanced undergraduate) classical mechanics courses (Pretty much all physicists in the world know this book). This latest edition is better equipped with advanced topics like chaos theory and fractals. I am aware of the fact that this book is present in the DISAT library, but they are not easily accessible (short hours, needs a department identification to get in).

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È il libro più recente e importnate sull’usa della diplomazia scientifica in Cina durante la Guerra Fredda. Importate per gli studi in storia della scienza e della tecnica portati avanti al Polito.

roberto DOT lalli AT polito DOT it

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This is probably the best beginner textbook covering the topic of special relativity with many applications. The best thing about this book is that it gives precise instructions on drawing the space-time diagram. In addition, this book encompasses great exercise problems on special relativity with a link to electromagnetism. I am aware that the book is present in DISAT library, but it is not easily accessible to undergraduate students.

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Usually, engineering students know nothing about analytical mechanics except for a few students who decide to take analytical mechanics courses. The mainstream textbooks taught physics from a Newtonian approach, using mostly vectors and potentials. When the students encounter Lagrangians and Hamiltonians they usually don’t understand the intricate mathematical foundations behind them. Unfortunately, many aspects of interesting theoretical physics are forbidden for engineering students: phase and configuration space, Noether’s theorem, Poincare’s methods, relativistic equations, Feynman’s quantum-mechanical interpretation of the principle of least action, and so on. There are several interesting features of this book. It explains the differences between variation and differentiation, something that most books on the subject leapfrog. It explains clearly the D’Alembert Principle and the Principle of Virtual Work (Often omitted at the undergraduate level). From those principles the author derives the Principle of Least Action (Hamiltonian Principle), using just elemental calculus. Then he introduces the reader to Legendre’s transformation and the relations between the two fundamental quantities of analytical mechanics: Lagrangian and Hamiltonian. In addition, equations of movement corresponding to those quantities: Euler-Lagrange (Lagrangian) and canonical (Hamiltonian) equations, a powerful insight into configuration and phase spaces, including the wonderful Liouville’s theorem, and
the analogies between optics and mechanics (Snell’s law) when he explains the Hamilton-Jabobi equations.

I can say that this is a defacto compendium of variational principles that we engineers take for granted despite its intricate nature. Of course, I don’t think there are going to be that many students at Politecnico who are going to be interested in reading this kind of somewhat pedantic subject. But who knows? One that the student who reads this might save humanity.

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Although this is the standard graduate-level or advanced undergraduate mathematics textbook designed for physicists, it is also suitable for engineers. This book explains the rudimentary concepts of tensor analysis in a no-nonsense way better than any other textbook. I know there are older editions of this book, but I couldn’t borrow it because the copy was severely damaged.

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Testo di grande itneresse per una ricerca in corso. Dall’abstract: “The book examines the unique role of European military engineers in the service of both kingdoms and republics from the fifteenth to the early nineteenth century […]. They were active in European sovereignties from Lisbon to Istanbul, and also in the fortified port enclaves and dominions acquired by their employers overseas […]. With the evolution of civilian professions such as civil engineering and pressure to specialise as combat engineers, they finally narrowed their scope, leading to underestimation of their wider earlier significance”.
Penso possa essere di interesse per entrambe le Biblioteche Centrali.

martino DOT pavignano AT polito DOT it

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This is a rare book on a rare topic: it is about ‘action’ and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian’ is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos’s book “The Variational Principles of Mechanics” (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out – it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

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