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The Princeton Colloquium
 
The Princeton Colloquium
Softcover ISBN:  978-0-8218-4641-4
Product Code:  COLL/3
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-3153-2
Product Code:  COLL/3.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Softcover ISBN:  978-0-8218-4641-4
eBook: ISBN:  978-1-4704-3153-2
Product Code:  COLL/3.B
List Price: $125.00 $95.00
MAA Member Price: $112.50 $85.50
AMS Member Price: $100.00 $76.00
The Princeton Colloquium
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The Princeton Colloquium
Softcover ISBN:  978-0-8218-4641-4
Product Code:  COLL/3
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-3153-2
Product Code:  COLL/3.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Softcover ISBN:  978-0-8218-4641-4
eBook ISBN:  978-1-4704-3153-2
Product Code:  COLL/3.B
List Price: $125.00 $95.00
MAA Member Price: $112.50 $85.50
AMS Member Price: $100.00 $76.00
  • Book Details
     
     
    Colloquium Publications
    Volume: 31913; 224 pp
    MSC: 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.

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 31913; 224 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.