B Bradie A Friendly Introduction To Numerical Analysis
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A Friendly Introduction to Numerical Analysis
An introduction to the fundamental concepts and techniques of numerical analysis and numerical methods. Application problems drawn from many different fields aim to prepare students to use the techniques covered to solve a variety of practical problems.
An Introduction To Applied Numerical Analysis
This book is based on lecture notes for a numerical analysis course designed mainly for senior undergraduate students majoring in mathematics, engineering, computer science and physical sciences.The book has two overarching goals. The first goal is to introduce different available numerical procedures for finding solutions to linear equations, roots of polynomial equations, interpolation and approximation, numerical differentiation and integration, differential equations, and error analysis. The second goal is to translate theory into practice through applying commonly used numerical methods in mathematics, physical sciences, biomedical sciences, and engineering.This book was crafted in an informal and user-friendly manner to motivate the study of the material being covered. Ample figures and numerical tables are presented to enhance the reader's ease of understanding of the material under consideration.
Numerical Mathematics
This textbook introduces key numerical algorithms used for problems arising in three core areas of scientific computing: calculus, differential equations, and linear algebra. Theoretical results supporting the derivation and error analysis of algorithms are given rigorous justification in the text and exercises, and a wide variety of detailed computational examples further enhance the understanding of key concepts. Numerical Mathematics includes topics not typically discussed in similar texts at this level, such as a Fourier-based analysis of the trapezoid rule, finite volume methods for the 2D Poisson problem, the Nyström method for approximating the solution of integral equations, and the relatively new FEAST method for targeting clusters of eigenvalues and their eigenvectors. An early emphasis is given to recognizing or deducing orders of convergence in practice, which is essential for assessing algorithm performance and debugging computational software. Numerical experiments complement many of the theorems concerning convergence, illustrating typical behavior of the associated algorithms when the assumptions of the theorems are satisfied and when they are not. This book is intended for advanced undergraduate and beginning graduate students in mathematics seeking a solid foundation in the theory and practice of scientific computing. Students and researchers in other disciplines who want a fuller understanding of the principles underlying these algorithms will also find it useful. The text is divided into three parts, corresponding to numerical methods for problems in calculus, differential equations, and linear algebra. Each part can be used for a one-term course (quarter or semester), making the book suitable for a two- or three-term sequence in numerical analysis or for largely independent courses on any of the three main topics.