Front Matter
BOOK I. GENERAL PROPERTIES OF CAUCHY’S PROBLEM
I. CAUCHY’S FUNDAMENTAL THEOREM CHARACTERISTICS
II. DISCUSSION OF CAUCHY’S RESULT
BOOK II. THE FUNDAMENTAL FORMULA AND THE ELEMENTARY SOLUTION
I. CLASSIC CASES AND RESULTS
II. THE FUNDAMENTAL FORMULA
III. THE ELEMENTARY SOLUTION
1. General Remarks
2. Solutions with an Algebroid Singularity
3. The Case of the Characteristic Conoid.The Elementary Solution
Additional Note on the Equations of Geodesics
BOOK III. THE EQUATIONS WITH AN ODD NUMBER OF INDEPENDENT VARIABLES
I. INTRODUCTION OF A NEW KIND OF IMPROPER INTEGRAL
1. Discussion of Preceding Results
2. The Finite Part of an Infinite Simple Integral
3. The Case of Multiple Integrals
4. Some Important Examples
II. THE INTEGRATION FOR AN ODD NUMBER OF INDEPENDENT VARIABLES
III. SYNTHESIS OF THE SOLUTION OBTAINED
IV. APPLICATIONS TO FAMILIAR EQUATIONS
BOOK IV. THE EQUATIONS WITH AN EVEN NUMBER OF INDEPENDENT VARIABLES AND THE METHOD OF DESCENT
I. INTEGRATION OF THE EQUATION IN 2m1 VARIABLES
1. General Formulæ
2. Familiar Examples
3. Application to a Discussion of Cauchy’s Problem
II. OTHER APPLICATIONS OF THE PRINCIPLE OF DESCENT
1. Descent from m Even to m Odd
2. Properties of the Coefficients in the Elementary Solution
3. Treatment of Non-Analytic Equations
INDEX
