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This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field-from Newton to Hamilton-while also painting a clear picture of the most modern developments.
The text is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications. Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material.
Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.
The text is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications. Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material.
Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.
From the reviews:
"By centering his presentation around the major aspects and omitting less important details, the author succeeds in providing a concise though lucid introduction into the mathematical areas ... it in particular, can be recommended to students who wish to learn these mathematical concepts without indulging too much in formal and technical points. ... The average graduate student ... will be well served by Romano's book. It enjoys many qualities that render this book a promising candidate for becoming a standard text in physics classrooms." (H. Hogreve, Mathematical Reviews, October, 2013)
"The author presents a high-level textbook based mainly on differential geometry methods; at the same time, he tries to follow a historical process that leads to an easier understanding of the development of mechanics. ... The book is written in a very clear and systematic manner; each chapter is followed by many exercises ... . The volume represents a real contribution to the field, being useful not only to students but to all readers who wish to have a correct and well-written information, too." (Petre P. Teodorescu, Zentralblatt MATH, Vol. 1263, 2013)
"By centering his presentation around the major aspects and omitting less important details, the author succeeds in providing a concise though lucid introduction into the mathematical areas ... it in particular, can be recommended to students who wish to learn these mathematical concepts without indulging too much in formal and technical points. ... The average graduate student ... will be well served by Romano's book. It enjoys many qualities that render this book a promising candidate for becoming a standard text in physics classrooms." (H. Hogreve, Mathematical Reviews, October, 2013)
"The author presents a high-level textbook based mainly on differential geometry methods; at the same time, he tries to follow a historical process that leads to an easier understanding of the development of mechanics. ... The book is written in a very clear and systematic manner; each chapter is followed by many exercises ... . The volume represents a real contribution to the field, being useful not only to students but to all readers who wish to have a correct and well-written information, too." (Petre P. Teodorescu, Zentralblatt MATH, Vol. 1263, 2013)