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## Physics for Mathematicians: Mechanics I (Hardback)"...I have written this work in order to learn the subject myself, in a form that I find comprehensible. And readers familiar with some of my previous books probably realize that this has pretty much been the reason for those works also." — Michael Spivak, Author, in the Preface (page vii) ## $76.95 |

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## Description

From the Preface: “The purpose of this book, or possibly series of books, is indicated precisely by the title *Physics for Mathematicians*. It is only necessary for me to explain what I mean by a mathematician, and what I mean by physics.

“By a mathematician I mean some one who has been trained in modern mathematics and been inculcated with its general outlook. No specific mathematical knowledge is expected, but for the purposes of this book on mechanics the material in *A Comprehensive Introduction to Differential Geometry*, Volumes 1 and 2, will generally be regarded as a prerequisite, not simply because I wrote this book, but because many of the concepts of mechanics are, in fact, best expressed in terms of basic differential geometric concepts. …

“And by physics I mean … well, physics, what physicists mean by physics, i.e., the actual study of physical objects, even wheels, weights, ropes and pulleys (rather than the study of symplectic structures on cotangent bundles, for example). In addition to presenting the advanced physics, which mathematicians find so easy, I also want to explore the workings of elementary physics, and the mysterious maneuvers—which physicists seem to find so natural—by which one reduces a complicated physical problem to a simple mathematical question, which I have always found so hard to fathom.”

**BRIEF CONTENTS**

In the Preface, the author beseeches the reader to try to solve all of the problems included at the end of the chapters. He states, “I should also point out that the problems are provided mainly to help in understanding basic points, or to mention additional topics, rather than to provide proficiency in solving physics problems, and their number decreases rather rapidly after Part I.”

**Part I. The Foundations of Mechanics**

- Newtonian Mechanics
- Newton’s Analysis of Central Forces
- Conservation Laws
- The One-Body and Two-Body Problems
- Rigid Bodies
- Constraints
- Philosophical and Historical Questions

**Part II. Building on the Foundations**

- Oscillations
- Rigid Body Motion
- Non-Inertial Systems and Fictitious Forces
- Friction, Friend and Foe

**Part III. Lagrangian Mechanics**

- Analytical Mechanics
- Variational Principles
- Small Oscillations

**Interlude**

- Light

**Part IV. Hamiltonian Mechanics**

- The Cotangent Bundle
- The Interplay of Mechanics and Optics
- Hamilton-Jacobi Theory
- Canonical Transformations
- Symplectic Manifolds
- Liouville Integrability
- Epilogue

The book concludes with Supplement: A PDE Primer, Bibliography, and Index.

- SKU:
- 2955
- Subject:
- Mechanics
- Author:
- Spivak, Michael
- Publisher:
- Publish or Perish
- Publish Date:
- 2010
- Format:
- Hardback
- Weight (pounds):
- 3.17
- Dimensions (W”xL”xH”):
- 6.7″x9.4″x1.8″
- ISBN-13:
- 9780914098324
- ISBN-10:
- 0914098322
- Grade Level:
- College

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