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mathematical beauty in physical world david oliver [pdf]

Mathematical Beauty in the Physical World (2nd Edition) by David Oliver

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About this book :-
Mathematical Beauty in the Physical World (2E) written by David Oliver .
The investigation of two bodies bound by an inverse-square-law field guides the reader of this book to the grand themes of contemporary mechanics, both classical (the Keplerian orbits of the Solar system) and quantum (the electron orbits in a hydrogen atom). Symmetries and invariants and the principles of least action and relativity provide simple, unifying approaches to a variety of topics. Thus, for example, the same four-dimensional rotational symmetry that yields closed orbits also unlocks the energy levels of the hydrogen atom. The elementary symmetries are broken at large speeds (leading in the sub-atomic case to the quantum field theories of elementary particles) and by the presence of other particles (leading in the classical case to chaotic orbits and the interplay of randomness and determinism). Mathematics is an essential part of physics, and the second half of the book expands on the mathematical aspects. Among them: - Noether
s theorem and the connection between invariance and symmetry.- The conection between the classical Poisson bracket and the quantum commutator. - And the unique role of the inverse-square forces in their ability to generate closed orbits and stable elements. No mathematical preparation beyond basic calculus is required to read this text. It should thus appeal not only to physics, chemistry and mathematics students, but also to other scientists interested in a unified portrait of classical and quantum mechanics.
This book celebrates an unassuming bit of physics that also turns out to be an inspiring teacher. The two-body problem - the motion of two bodies bound by the inverse-square force of gravity and electricity - is the Shaggy Steed of physics, guiding the reader to an understanding of both the forces and the mathematical beauty hidden in the physical world.

Book Detail :-
Title: Mathematical Beauty in the Physical World
Edition: Second Edition
Author(s): David Oliver
Publisher: Springer
Series:
Year: 2003
Pages: 319
Type: PDF
Language: English
ISBN: 0387403078
Country: German
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About Author :-
The author David Oliver (1862 – 1943) was a German mathematician and one of the most influential mathematicians. Hilbert area of work was invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).

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Book Contents :-
Mathematical Beauty in the Physical World (2E) written by David Oliver cover the following topics. '
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
1. The Shaggy Steed of Physics
2. The Heavens and the Elements
3. The Law of Motion
4. Classical Mechanics: the Heavens
5. Quantum Mechanics: the Elements
6. The Hidden Unity of Space and Time
7. The Manifold Universe
People
Notes
Index


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