Ref.

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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Ref.

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.

s260250 AT studenti DOT polito DOT it

Ref.

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.

s260250 AT studenti DOT polito DOT it

Ref.

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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Ref.

Richard Feynman is an American physicist who is famous in a number of dimensions. To scientists, he is a giant of 20th-century physics and a pioneer of quantum electrodynamics (QED). To the public, he is a refreshing character that went against the typical stereotype of physicists. To physics students, he was an exceptionally excellent teacher, both for his charisma and his uncanny ability to make complicated topics feel natural and intuitive. Although many of the lectures he gave at Caltech are immortalized in his three-volume series “The Feynman Lectures on Physics.” Unfortunately, not all of the lectures he gave made it to this series. In particular, a guest lecture given on March 13, 1964, entitled “The Motion of Planets around the Sun” was lost because it was somehow buried in the office of one of Feynman’s colleagues. The lecture notes were later found and restored by Caltech physicist David L. Goodstein and his wife, who worked at Caltech as an archivist. Eventually, it was published in a book titled “Feynman’s Lost Lecture,” which contains both the lecture itself and the surrounding stories in a beautiful way. The lecture mainly tries to answer the question “Why are orbits elliptic?” There is an analytical solution involving pedantic mathematical formulas, but Feynman did something special by providing a very elementary approach to answering the question. It would be a nice supplement for some students taking Physics I course since Physics I never really answers the cause of the elliptic orbits of planets.

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This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students or advanced undergraduate students. The best part of this book is how well it interlocks the very palpable concepts of mathematics such as chaos, fractals, and dynamical systems to abstract pure mathematics. It makes it an interesting text for both engineers and pure/applied mathematicians. It was even recommended by my Mathematical Analysis II (Analisi Matematica II) instructor.

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Books usually cannot replace passionate and inspiring lecturers. However, I think this book gets quite close. This the most authoritative and accessible single-volume reference book on applied mathematics really demonstrates underlying mathematical principles that serve as cornerstones for many areas, including, but not limited to engineering. In addition, it simultaneously seves as a good and quick reference book for recaping.

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This is what I wish I learned from in my first year. Honestly, the third of it that is about linear algebra is one of the best linear algebra resources out there. It doesn’t pull any punches for the pure math students, but unlike many books with that target audience it stays grounded in frequent numerical examples and scientific applications. The culmination to the generalized Stokes’ theorem, as well as the way to frame Maxwell’s equations with differential forms, are particularly satisfying.

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The solid state physics could be one of the most daunting topics in physics and engineering , but destined to be encountered. This book presents all of the topics in undergraduate-level solid state physics in a clear fashion, dense with explanatory or just plain entertaining footnotes, which makes it much more appropriate for beginners than the academia standard Kittel’s “Solid State Physics.” This may be the best introductory book for learning solid state physics. It is certainly the most fun to read. In addition, this book delves deep into the topics related to magnetic materials (not trivial topics as people think), which are often discussed in facile manner in Politecnico’s Physics II (Fisica II) courses.

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After studying electromagnetism and fluid mechanics, maybe there are some students who possess uncanny inclination to amalgamate those two disciplines. This book might fulfill those students’ insatiable desire to “mix” disciplines and lead them to studying MHD and plasma physics, one of the fields with bright prospect. This book is intended to serve as an introductory text for advanced undergraduates and postgraduate students in physics, applied mathematics and engineering. The material in the text is heavily weighted towards incompressible flows and to terrestrial (as distinct from astrophysical) applications. The final sections of the text also contain an outline of the latest advances in the metallurgical applications of MHD and so are relevant to professional researchers in applied mathematics, engineering and metallurgy.

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