Lectures on Cauchy's Problem in Linear Partial Differential Equations

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Courier Dover Publications, 2003 - Mathematics - 316 pages
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Would well repay study by most theoretical physicists."--Physics Today

"An overwhelming influence on subsequent work on the wave equation."--Science Progress

"One of the classical treatises on hyperbolic equations."--Royal Naval Scientific Service

Delivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations instead of only to one. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations with an even number of independent variables and the method of descent. 1923 ed.
  

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Contents

CAUCHYS FUNDAMENTAL THEOREM CHARACTER
3
DISCUSSION OF CAUCHYS RESULT
23
CLASSIC CASES AND RESULTS
47
THE FUNDAMENTAL FORMULA
58
THE ELEMENTARY SOLUTION
70
INTRODUCTION OF A NEW KIND OF IMPROPER
117
THE INTEGRATION FOR AN ODD NUMBER OF INDE
159
SYNTHESIS OF THE SOLUTION OBTAINED
181
APPLICATIONS TO FAMILIAR EQUATIONS
207
THE EQUATIONS WITH AN EVEN NUMBER
213
OTHER APPLICATIONS OF THE PRINCIPLE OF DESCENT
262
INDEX
313
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