A Course on Integral Equations
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences ( AMS) series, which will focus on advanced textbooks and research level monographs. Foreword This book is based on a one-semester course for graduate students in the physical sciences and applied mathematics. No great mathematical back ground is needed, but the student should be familiar with the theory of analytic functions of a complex variable. Since the course is on problem solving rather than theorem-proving, the main requirement is that the stu dent should be willing to work out a large number of specific examples.
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absolutely convergent absolutely integrable approaches zero approximation arbitrary associated analytic function asymptotic averager bounded coefficient completely monotone consider eigenfunctions eigenvalue eigenvectors essential singularity Evaluate example exponential order finite interval finite-dimensional Fourier Fredholm condition Fredholm equation Fredholm theory gives half-plane function half-plane of convergence homogeneous equation infinite infinity integral converges integral equation integral operator integration contour inversion contour inversion integral J—oo Laplace integral Laplace transform lhp functions limit linear combination linearly independent loop integral lower half-plane matrix negative Neumann series non-unique norm obtain one-sided orthogonal orthonormal system p(oo Plemelj formulas polynomial principal value integral problem prove radius of convergence Rayleigh quotient Re(s real axis reciprocal kernel regularly-varying result right half-plane right-most singularity satisfied second kind separable kernel sequence simple pole solution solve suppose symmetric theorem two-sided Laplace transform uniqueness upper half-plane valid vanish vectors w+(x w+(z
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Encyclopedia of physical science and technology, Volume 7
Robert Allen Meyers
Snippet view - 2002