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Numerical analysis --- 517 --- Analysis --- Numerical analysis. --- 517 Analysis --- Mathematical analysis
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Mathematical analysis. --- Analyse mathématique --- 517.1 --- 517 --- 517 Analysis --- Analysis --- 517.1 Mathematical analysis --- Mathematical analysis
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517 --- Uitvoeringspraktijk --- Barok --- 18e eeuw --- 17e eeuw
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Mathematical analysis. --- 517 --- 51-74 --- 517 Analysis --- Analysis --- 51-74 Mathematics--?-74 --- Mathematics--?-74 --- Mathematical analysis --- 517.1 Mathematical analysis --- 517.1. --- 517.1 --- Mathématiques --- Mathematics --- Analyse mathématique --- Engineering. --- Mathematics. --- Analyse mathématique --- Mathématiques --- Methodes mathematiques de la physique
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This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. The book can be used in an honor calculus sequence typically taken by freshmen planning to major in engineering, mathematics, and science, or in an introductory course in rigorous real analysis offered to mathematics majors. Donald Estep is Professor of Mathematics at Colorado State University. He is the author of Computational Differential Equations, with K. Eriksson, P. Hansbo and C. Johnson (Cambridge University Press 1996) and Estimating the Error of Numerical Solutions of Systems of Nonlinear Reaction-Diffusion Equations with M. Larson and R. Williams (A.M.S. Memoirs, 2000), and recently co-edited Collected Lectures on the Preservation of Stability under Discretization, with Simon Tavener (S.I.A.M., 2002), as well as numerous research articles. His research interests include computational error estimation and adaptive finite element methods, numerical solution of evolutionary problems, and computational investigation of physical models.
Mathematical analysis --- 517.1 --- 517.1 Mathematical analysis --- 517.1 Introduction to analysis --- Introduction to analysis --- Mathematical analysis. --- Analyse mathématique --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Analysis (Mathematics). --- Analysis. --- 517.1. --- Global analysis (Mathematics).
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The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers). To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions. Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail. The presentation of probability has been reorganised and greatly extended, and includes all physically important distributions. New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F-tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting. In other chapters the following topics have been added: linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods.
Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis
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517.53 --- Functions of complex variables --- Mathematical analysis --- 517.1 Mathematical analysis --- Complex variables --- 517.53 Functions of a complex variable --- Functions of a complex variable --- Elliptic functions --- Functions of real variables --- 517.1. --- Functions of complex variables. --- Mathematical analysis. --- Fonctions d'une variable complexe --- Analyse mathématique --- Analyse mathématique --- Fonctions d'une variable complexe. --- Analyse mathématique. --- 517.1
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Mathematical analysis --- Calculus --- Calcul infinitésimal --- Problems, exercises, etc. --- Problèmes et exercices --- Wiskunde --- 517 --- wiskundige functies --- Analysis --- 517 Analysis --- Calcul infinitésimal --- Problèmes et exercices
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