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salgado classical numerical analysis comprehen course 2023

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Textbook in PDF format Numerical Analysis is a broad field, and coming to grips with all of it may seem like a daunting task. This text provides a thorough and comprehensive exposition of all the topics contained in a classical graduate sequence in numerical analysis. With an emphasis on theory and connections with linear algebra and analysis, the book shows all the rigor of numerical analysis. Its high level and exhaustive coverage will prepare students for research in the field and become a valuable reference as they continue their career. Students will appreciate the simple notation, clear assumptions and arguments, as well as the many examples and classroom-tested exercises ranging from simple verification to qualifying exam-level problems. In addition to the many examples with hand calculations, readers will also be able to translate theory into practical computational codes by running sample MATLAB codes as they try out new concepts. Preface Acknowledgments Symbols Numerical Linear Algebra Linear Operators and Matrices The Singular Value Decomposition Systems of Linear Equations Norms and Matrix Conditioning Linear Least Squares Problem Linear Iterative Methods Variational and Krylov Subspace Methods Eigenvalue Problems Constructive Approximation Theory Polynomial Interpolation Minimax Polynomial Approximation Polynomial Least Squares Approximation Fourier Series Trigonometric Interpolation and the Fast Fourier Transform Numerical Quadrature Nonlinear Equations and Optimization Solution of Nonlinear Equations Convex Optimization Initial Value Problems for Ordinary Differential Equations Initial Value Problems for Ordinary Di erential Equations Single-Step Methods Runge-Kutta Methods Linear Multi-step Methods Stiff Systems of Ordinary Differential Equations and Linear Stability Galerkin Methods for Initial Value Problems Boundary and Initial Boundary Value Problems Boundary and Initial Boundary Value Problems for Partial Di erential Equations Finite Difference Methods for Elliptic Problems Finite Element Methods for Elliptic Problems Spectral and Pseudo-Spectral Methods for Periodic Elliptic Equations Collocation Methods for Elliptic Equations Finite Difference Methods for Parabolic Problems Finite Difference Methods for Hyperbolic Problems Appendix A Linear Algebra Review Appendix B Basic Analysis Review Appendix C Banach Fixed Point Theorem Appendix D A (Petting) Zoo of Function Spaces References Index

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Salgado A. Classical Numerical Analysis.A Comprehen. Course 2023.pdf 16.5 MB

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salgado classical numerical analysis comprehen course 2023