This book provides professionals and students with a thorough understanding of the interface between mathematics and scientific computation. Ranging from classical questions to modern techniques, it explains why numerical computations succeed or fail. The book is divided into four sections, with an emphasis on the use of mathematics as a tool in determining the success rate of numerical methods. The text requires only a modest level of mathematical training, and is ideally suited for scientists and students in mathematics, physics and engineering.
This book provides professionals and students with a thorough understanding of the interface between mathematics and scientific computation. Ranging from classical questions to modern techniques, it explains why numerical computations succeed or fail. The book is divided into four sections, with an emphasis on the use of mathematics as a tool in determining the success rate of numerical methods. The text requires only a modest level of mathematical training, and is ideally suited for scientists and students in mathematics, physics and engineering.
Part I: The entrance fee 1: Floating numbers 2: A flavour of numerical analysis 3: Algebraic preliminaries Part II: Polynomial and trigonometric approximation of functions 4: Interpolation and divided differences 5: Least squares for polynomials 6: Splines 7: Fourier's world 8: Quadrature Part III: Numerical linear algebra 9: Gauss' world 10: Theoretical interlude 11: Iterations and recurrences 12: Pythagoras' world Part IV: Non-linear problems 13: Spectra 14: Non-linear equations and systems 15: Solving differential systems 16: Single step schemes 17: Linear multi-step schemes 18: Toward partial differential equations Bibliography Index
Part I: The entrance fee 1: Floating numbers 2: A flavour of numerical analysis 3: Algebraic preliminaries Part II: Polynomial and trigonometric approximation of functions 4: Interpolation and divided differences 5: Least squares for polynomials 6: Splines 7: Fourier's world 8: Quadrature Part III: Numerical linear algebra 9: Gauss' world 10: Theoretical interlude 11: Iterations and recurrences 12: Pythagoras' world Part IV: Non-linear problems 13: Spectra 14: Non-linear equations and systems 15: Solving differential systems 16: Single step schemes 17: Linear multi-step schemes 18: Toward partial differential equations Bibliography Index
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