- Published Year: 2010
- Page count: 530
- File Size: 42 Mb
- Language: English
- Published by: Springer-Verlag.
- Visited by: 5
- Rating/Review: 4.7
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ISBN:
9781441930873
9781475720631
1441930876
Keywords:
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Learn MoreMathematical methods of classical mechanics: with 269 illustrations
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Each download or ask from book AI costs 2 points. To earn more free points, please visit the Points Guide Page and complete some valuable actions.Introduction to 'Mathematical Methods of Classical Mechanics'
Written by Vladimir Igorevich Arnolʹd, with contributions from Alan Weinstein and Karen Vogtmann, "Mathematical Methods of Classical Mechanics" presents an increasing complexity in understanding the nature and mathematical backbone of classical mechanics. This profound work offers a multitude of insights, systematically presented with clarity, rigor, and a wealth of illustrative examples, annotated equations, and diagrams — a total of 269 illustrations that complement the textual content.
Detailed Summary of the Book
This book is extensively organized, starting with preliminary aspects of mechanics in readable mathematical forms. Vladimir Igorevich Arnolʹd draws from fundamental elements of differential calculus to explain dynamics and motions. The text is carefully laid out to ensure that progression through simple to complex topics is seamless. Initial chapters focus on introducing the key principles of Newtonian mechanics, as denoted by formulations and Hamiltonian dynamics.
As the reader progresses, the book unravels advanced topics such as symplectic manifolds, Hamilton-Jacobi theory, and instability in Hamiltonian systems. It encapsulates essential theorems and proofs integral to mechanics, while inspiring an intuitive grasp of mathematical methods in theoretical physics. Important concepts such as Lagrangian and Hamiltonian formalism are addressed in a way that appeals both to mathematicians and physicists.
Key Takeaways
- Comprehensive understanding of classical mechanics using advanced mathematical techniques.
- Development and application of rigorous mathematical proofs to theories of motion and force.
- Illustrative examples that highlight theoretical insights and simplify complex ideas.
- Integration of theoretical mechanics with practical illustrative diagrams aids comprehensive learning.
- Insight into the relationship between mechanics and broader fields such as quantum mechanics and general relativity.
Famous Quotes from the Book
"Classical mechanics only deals with the macroscopic behavior of matter and forces, yet the mathematical precision required for mastering it is profound and applicable in advanced fields."
"The symplectic structure is to mechanics what the metric is to geometry; each system speaks its language, yet congruence exists in their essence."
Why This Book Matters
"Mathematical Methods of Classical Mechanics" holds significant relevance in the domain of physics and mathematics because it bridges abstract mathematical theory with tangible mechanical concepts. The influence of this book is widespread, touching upon new generations of students, educators, and researchers who seek a more profound understanding of classical mechanics through mathematical frameworks. Its methodical approach contributes to the foundation necessary for exploring myriad applications in physics, engineering, and emerging interdisciplinary fields. The work of Vladimir Igorevich Arnolʹd in this context signifies notable progress in how mathematical frameworks can be effectively woven into the tapestry of classical physics, making it a timeless resource.
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