Courier Corporation, 1 mars 1985 - 238 pages
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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Symmetric Kernels and Orthogonal Systems of Functions
Some Types of Singular or NonLinear Integral Equations
Autres éditions - Tout afficher
algebraic already analysis analytic function applications approximation arbitrary assume basic interval becomes belongs boundary bounded called closed coefficients complete condition Consequently consider constant continuous converges corresponding deduced denotes determinant differential equation difficulty eigenfunctions eigenvalues equality everywhere example existence fact finite follows formula Fourier Fredholm Fredholm integral equation function f(x given gives Hence identically immediately important independent inequality infinite series instance integral equation INTRODUCTION iterated kernels least limit linear Math mathematical means method Moreover necessarily non-linear observe obtain obviously ON-system orthogonal particular polynomials positive possible previous section problem proof prove reduced resolvent kernel respectively satisfies second kind shows side similar simple singular solution solved successive sufficient suitable symmetric kernel theorem theory transformation uniformly unknown valid values vanishes Volterra integral equation write zero