A01=Edward Kasner
A01=Gilbert Ames Bliss
Author_Edward Kasner
Author_Gilbert Ames Bliss
Category=PB
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Product details
- ISBN 9780821846414
- Weight: 425g
- Publication Date: 30 Jul 1913
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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' ""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.
