Water Waves: The Mathematical Theory with Applications

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John Wiley & Sons, Apr 16, 1992 - Mathematics - 600 pages
Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.
 

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Contents

Introduction
vii
PART I
1
Basic Hydrodynamics
3
The Two Basic Approximate Theories
19
PART II
33
Simple Harmonic Oscillations in Water of Constant Depth
37
Waves Maintained by Simple Harmonic Surface Pressure in Water of Uniform Depth Forced Oscillations
55
Waves on Sloping Beaches and Past Obstacles
69
Twodimensional Waves on a Running Stream in Water of Uniform Depth
198
Waves Caused by a Moving Pressure Point Kelvins Theory of the Wave Pattern Created by a Moving Ship
219
The Motion of a Ship as a Floating Rigid Body in a Seaway
245
PART III
289
Long Waves in Shallow Water
291
Mathematical Hydraulics
451
PART IV
511
Problems in which Free Surface Conditions are Satisfied Exactly The Breaking of a Dam LeviCivitas Theory
513

Unsteady Motions
149

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About the author (1992)

James J Stoker was an American applied mathematician and engineer. He was director of the Courant Institute of Mathematical Sciences and is considered one of the founders of the institute, Courant and Friedrichs being the others. Stoker is known for his work in differential geometry and theory of water waves.

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