First published in 1914, as the second edition of a 1909 original, this book forms number ten in the Cambridge Tracts in Mathematics and Mathematical Physics series. It was written to provide readers with 'the main portions of the theory of integral equations in a readable and, at the same time, accurate form, following roughly the lines of historical development'. Textual notes are incorporated throughout. This book will be of value to anyone with an interest in integral equations and the history of mathematics.
First published in 1914, as the second edition of a 1909 original, this book forms number ten in the Cambridge Tracts in Mathematics and Mathematical Physics series. It was written to provide readers with 'the main portions of the theory of integral equations in a readable and, at the same time, accurate form, following roughly the lines of historical development'. Textual notes are incorporated throughout. This book will be of value to anyone with an interest in integral equations and the history of mathematics.
Introduction 1. Some preliminary propositions and definitions 2. Abel's mechanical problem 3. Solution of Abel's equation 4. Liouville's introduction of integral equations of the second kind 5. The method of successive substitutions 6. Voltera's treatment of equations of the second kind. Iterated and reciprocal functions 7. Linear equations with an infinite number of variables 8. Fredholm's solution 9. The integral equation with a parameter 10. The fundamental theorem concerning homogeneous integral equations, with some applications 11. Symmetric kernels 12. Orthogonal functions 13. The integral equation of the first kind whose kernel is finite 14. Equations of the first kind whose kernel or whose interval is not finite Index.
Introduction 1. Some preliminary propositions and definitions 2. Abel's mechanical problem 3. Solution of Abel's equation 4. Liouville's introduction of integral equations of the second kind 5. The method of successive substitutions 6. Voltera's treatment of equations of the second kind. Iterated and reciprocal functions 7. Linear equations with an infinite number of variables 8. Fredholm's solution 9. The integral equation with a parameter 10. The fundamental theorem concerning homogeneous integral equations, with some applications 11. Symmetric kernels 12. Orthogonal functions 13. The integral equation of the first kind whose kernel is finite 14. Equations of the first kind whose kernel or whose interval is not finite Index.
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