This 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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analytic function applied approximation arbitrary constant asymptotic basic interval belongs boundary conditions calculated Carleman class Lz Consequently consider corresponding deduced denotes determinant eigenfunctions eigenvalues example exists fact finite follows formula Fourier coefficients Fredholm equations Fredholm integral equation Fredsslm function f(x fusstion given equation Green's formula Green's function Hence hesse Hilbert-Schmidt theorem homogeneous equation hypothesis important infinite number infinite series iterated kernels kernel K(x La-function linear combination linear differential equation linearly independent Lz-function Lz-kernel Math mathematical membrane Mercer's theorem method metssd Moreover non-homogeneous non-linear integral equation non-trivial solutions obtain ON-system orthogonal Parseval's polynomials previous section problem prove resolvent kernel respectively Riesz-Fischer theorem right-hand side satisfies condition Schwarz inequality second kind shows singular solved ssmogeneous sssw suitable symmetric kernel term triangular kernel Tricomi uniformly convergent upper bound valid values vani-es vibrations Volterra Equations Volterra integral equation zero