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. |
Contents
| 1 | |
Fredholm Equations e | 49 |
Symmetric Kernels and Orthogonal Systems of Functions | 81 |
PGKernels | 98 |
Some Types of Singular or NonLinear Integral Equations 16 1 | 161 |
Algebraic Systems of Linear Equations | 219 |
Exercises | 227 |
| 235 | |
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a)da analytic function approximation arbitrary constant asymptotic basic interval belongs Bessel functions boundary conditions Consequently consider convergent series corresponding deduced denotes determinant Dirichlet problem eigenfunctions eigenvalue A1 eigenvalues fact finite follows formula Fourier coefficients Fredholm equation Fredholm integral equation function f(a function ºf given equation given function H(ac Hence Hilbert-Schmidt theorem homogeneous equation hypothesis infinite number infinite series iterated kernels K(ac kernel K(x La-function La-kernel linear combination linear differential equation linearly independent Math membrane method Moreover non-homogeneous non-linear integral equation non-trivial solutions º e º º º obtain ºff ON-system orthogonal PG-kernel polynomials previous section problem prove quadratically quadratically integrable resolvent kernel respectively Riesz-Fischer theorem right-hand side satisfies condition Schwarz inequality second kind shows singular ſº solved suitable symmetric kernel transformation triangular kernel Tricomi uniformly convergent values vanish almost everywhere Volterra integral equation zero