The book offers a comprehensive guide to the numerical methods used for solving a wide range of integral equations. It covers various techniques and approaches, making it a valuable resource for those looking to understand and apply these mathematical concepts effectively.
This edition of the standard introductory textbook on numerical analysis has been revised and updated to include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines and boundary value problems.
These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.
This text gives an introduction to functional analysis for graduate students pursuing research involving numerical analysis. The text covers basic results of functional analysis as well as additional topics needed in theoretical numerical analysis. Applications of this functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. Extensive exercises are included at the end of each section along with recommendations for additional reading. This book is especially suited to students interested in the numerical solution of differential and/or integral equations, but it should appeal to numerical analysts and mathematically-oriented students and researchers in engineering, physics, and related areas.