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Softcover ISBN:  9780821846414 
Product Code:  COLL/3 
List Price:  $65.00 
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AMS Member Price:  $52.00 
eBook ISBN:  9781470431532 
Product Code:  COLL/3.E 
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AMS Member Price:  $48.00 
Softcover ISBN:  9780821846414 
eBook ISBN:  9781470431532 
Product Code:  COLL/3.B 
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Book DetailsColloquium PublicationsVolume: 3; 1913; 224 ppMSC: Primary 34; 35; 37; 70
Following the early tradition of the American Mathematical Society, the sixth colloquium of the Society was held as part of the summer meeting that took place at Princeton University. Two sets of lectures were presented: Fundamental Existence Theorems, by G. A. Bliss, and Geometric Aspects of Dynamics, by Edward Kasner.
The goal of Bliss's Colloquium Lectures is an overview of contemporary existence theorems for solutions to ordinary or partial differential equations. The first part of the book, however, covers algebraic and analytic aspects of implicit functions. These become the primary tools for the existence theorems, as Bliss builds from the theories established by Cauchy and Picard. There are also applications to the calculus of variations.
Kasner's lectures were concerned with the differential geometry of dynamics, especially kinetics. At the time of the colloquium, it was more common in kinematics to consider geometry of trajectories only in the absence of an external force. The lectures begin with a discussion of the possible trajectories in an arbitrary force field. Kasner then specializes to the study of conservative forces, including wave propagation and some curious optical phenomena. The discussion of constrained motions leads to the brachistochrone and tautochrone problems. Kasner concludes by looking at more complicated motions, such as trajectories in a resisting medium.
ReadershipGraduate students and research mathematicians interested in fundamental existence theorems and geometric aspects of dynamics.

Table of Contents

Chapters

Introduction

Chapter I. TRAJECTORIES IN AN ARBITRARY FIELD OF FORCE

Chapter II. NATURAL FAMILIES: THE GEOMETRY OF CONSERVATIVE FIELDS OF FORCE

Chapter III. TRANSFORMATION THEORIES IN DYNAMICS

Chapter IV. CONSTRAINED MOTIONS IN A FIELD. GENERALIZATION OF THE TRAJECTORY PROBLEM INCLUDING BRACHISTOCHRONES AND CATENARIES

Chapter V. MORE COMPLICATED TYPES OF FORCE


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Following the early tradition of the American Mathematical Society, the sixth colloquium of the Society was held as part of the summer meeting that took place at Princeton University. Two sets of lectures were presented: Fundamental Existence Theorems, by G. A. Bliss, and Geometric Aspects of Dynamics, by Edward Kasner.
The goal of Bliss's Colloquium Lectures is an overview of contemporary existence theorems for solutions to ordinary or partial differential equations. The first part of the book, however, covers algebraic and analytic aspects of implicit functions. These become the primary tools for the existence theorems, as Bliss builds from the theories established by Cauchy and Picard. There are also applications to the calculus of variations.
Kasner's lectures were concerned with the differential geometry of dynamics, especially kinetics. At the time of the colloquium, it was more common in kinematics to consider geometry of trajectories only in the absence of an external force. The lectures begin with a discussion of the possible trajectories in an arbitrary force field. Kasner then specializes to the study of conservative forces, including wave propagation and some curious optical phenomena. The discussion of constrained motions leads to the brachistochrone and tautochrone problems. Kasner concludes by looking at more complicated motions, such as trajectories in a resisting medium.
Graduate students and research mathematicians interested in fundamental existence theorems and geometric aspects of dynamics.

Chapters

Introduction

Chapter I. TRAJECTORIES IN AN ARBITRARY FIELD OF FORCE

Chapter II. NATURAL FAMILIES: THE GEOMETRY OF CONSERVATIVE FIELDS OF FORCE

Chapter III. TRANSFORMATION THEORIES IN DYNAMICS

Chapter IV. CONSTRAINED MOTIONS IN A FIELD. GENERALIZATION OF THE TRAJECTORY PROBLEM INCLUDING BRACHISTOCHRONES AND CATENARIES

Chapter V. MORE COMPLICATED TYPES OF FORCE