**Colloquium Publications**

Volume: 3;
1913;
224 pp;
Softcover

MSC: Primary 34; 35; 37; 70;

Print ISBN: 978-0-8218-4641-4

Product Code: COLL/3

List Price: $58.00

Individual Member Price: $46.40

**Electronic ISBN: 978-1-4704-3153-2
Product Code: COLL/3.E**

List Price: $58.00

Individual Member Price: $46.40

# The Princeton Colloquium

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*Gilbert Ames Bliss; Edward Kasner*

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

# Table of Contents

## The Princeton Colloquium

- Cover Cover11
- Title page i2
- Contents iii4
- Introduction 16
- Chapter I. TRAJECTORIES IN AN ARBITRARY FIELD OF FORCE 712
- Chapter II. NATURAL FAMILIES: THE GEOMETRY OF CONSERVATIVE FIELDS OF FORCE 3540
- Chapter III. TRANSFORMATION THEORIES IN DYNAMICS 7479
- Chapter IV. CONSTRAINED MOTIONS IN A FIELD. GENERALIZATION OP THE TRAJECTORY PROBLEM INCLUDING BRACHISTOCHRONES AND CATENARIES 9297
- Chapter V. MORE COMPLICATED TYPES OP FORCE 104109
- Back Cover Back Cover1235