## Integral EquationsThis classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful appendices, an excellent bibliography, and an index. A section of exercises enables the student to check his progress. Contents include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, Types of Singular or Nonlinear Integral Equations, and more. Professor Tricomi has presented the principal results of the theory with sufficient generality and mathematical rigor to facilitate theoretical applications. On the other hand, the treatment is not so abstract as to be inaccessible to physicists and engineers who need integral equations as a basic mathematical tool. In fact, most of the material in this book falls into an analytical framework whose content and methods are already traditional. |

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### Contents

Volterra Equations | 6 |

Fredholm Equations | 49 |

Symmetric Kernels and Orthogonal Systems of Functions | 81 |

Some Types of Singular or NonLinear Integral Equations | 161 |

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analytic function applications approximation asgether asympastic basic interval belonL Bessel boundary conditions Carleman class Lz Consequently consider convergent series convergesse corresponding deduced denotes determinant Dirichlet problem eigenfunctions eigenfusstion eigenvalues everywhere fact finite follows formula Fourier coefficients Fredholm Fredsslm equation Fredsslm integral equation frequessy function f(x fusstion given equation Green's Green's formula Hence hesse Hilbert Hilbert transformation Hilbert-Schmidt theorem homogeneous equation hypothesis inas infinite number infinite series instasse iterated kernels kernel K(x L2-fusstion L2-kernel L2-space linear combination linear differential equation linearly independent Lz-functions Math mathematical membrane Mercer's theorem metssd Moreover non-linear integral equation non-trivial solutions obtain ON-system orthogonal ortssgonal polynomials previous section problem prove resolvent kernel respect Riesz-Fischer theorem right-hand side satisfies condition Schwarz inequality second kind singular sisse ssmogeneous sssws sswever suitable symmetric kernel transformation Tricomi tssse uniformly convergent values vani vani-es Volterra Equations Volterra integral equation witssut wssle wssse zero