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Preface | iii | |
Book I. | General Properties of Cauchy's Problem | |
I. | Cauchy's Fundamental Theorem. Characteristics | 3 |
II. | Discussion of Cauchy's Result | 23 |
Book II. | The Fundamental Formula and the Elementary Solution | |
I. | Classic Cases and Results | 47 |
II. | The Fundamental Formula | 58 |
III. | The Elementary Solution | 70 |
1. | General Remarks | 70 |
2. | Solutions with an Algebroid Singularity | 73 |
3. | The Case of the Characteristic Conoid | 83 |
Additional Note on the Equations of Geodesics | 111 | |
Book III. | The Equations with an Odd Number of Independent Variables | |
I. | Introduction of a New Kind of Improper Integral | 117 |
1. | Discussion of Preceding Results | 117 |
2. | The Finite Part of an Infinite Simple Integral | 133 |
3. | The Case of Multiple Integrals | 141 |
4. | Some Important Examples | 150 |
II. | The Integration for an Odd Number of Independent Variables | 159 |
III. | Synthesis of the Solution Obtained | 181 |
IV. | Applications to Familiar Equations | 207 |
Book IV. | The Equations with an Even Number of Independent Variables and the Method of Descent | |
I. | Integration of the Equation in 2m[subscript 1] Variables | 215 |
1. | General Formulae | 215 |
2. | Familiar Examples | 236 |
3. | Application to a Discussion of Cauchy's Problem | 247 |
II. | Other Applications of the Principle of Descent | 262 |
1. | Descent from m Even to m Odd | 262 |
2. | Properties of the Coefficients in the Elementary Solution | 266 |
3. | Treatment of Non-Analytic Equations | 277 |
Index | 313 |
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Add Lectures on Cauchy's Problem in Linear Partial Differential Equations, Delivered at Columbia University and the Universities of Rome and Zurich, 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 wo, Lectures on Cauchy's Problem in Linear Partial Differential Equations to the inventory that you are selling on WonderClubX
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Add Lectures on Cauchy's Problem in Linear Partial Differential Equations, Delivered at Columbia University and the Universities of Rome and Zurich, 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 wo, Lectures on Cauchy's Problem in Linear Partial Differential Equations to your collection on WonderClub |