Classical Mechanics with Mathematica®
(Sprache: Englisch)
Valuable for its wide-ranging yet thorough approach to mechanics, this textbook succeeds in bridging the often daunting divide between classical analytical and modern differential geometries, and reflects the author's decades-long teaching experience.
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Produktinformationen zu „Classical Mechanics with Mathematica® “
Valuable for its wide-ranging yet thorough approach to mechanics, this textbook succeeds in bridging the often daunting divide between classical analytical and modern differential geometries, and reflects the author's decades-long teaching experience.
Klappentext zu „Classical Mechanics with Mathematica® “
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 author from 35 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 Lagrange-while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica .The volume 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.
Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.
Inhaltsverzeichnis zu „Classical Mechanics with Mathematica® “
I Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Tensors.- 6 Differentiable Manifolds.- 7 One-Parameter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Differential Calculus.- 10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Principles of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dynamics.- 16 Dynamics of a Rigid Body.- 17 Lagrangian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrable Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics.- A First-Order PDE.- B Fourier's Series.- References.- Index.
Autoren-Porträt von Antonio Romano
Antonio Romano has been the author or coauthor of numerous books on mechanics and Mathematica, and he has taught courses in mechanics for 35 years at "Il Fredrico" University in Naples.
Bibliographische Angaben
- Autor: Antonio Romano
- 2012, 2012., 506 Seiten, 127 Schwarz-Weiß-Abbildungen, Maße: 16,4 x 24,3 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0817683518
- ISBN-13: 9780817683511
- Erscheinungsdatum: 31.10.2012
Sprache:
Englisch
Rezension zu „Classical Mechanics with Mathematica® “
From the reviews:"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)
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