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This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Gdel on recent mathematical study.

Mathematics --- Mathematical analysis --- 517.1 Mathematical analysis --- Math --- Science --- History. --- Mathématiques --- History --- Histoire. --- Mathématiques --- Histoire --- Mathematics - History

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Mathematical analysis --- Analyse mathématique --- Problems, exercises, etc --- Problèmes et exercices --- -Advanced calculus --- Analysis (Mathematics) --- Algebra --- Problems, exercises, etc. --- -517.1 Mathematical analysis --- -Problems, exercises, etc --- Analyse mathématique --- Problèmes et exercices --- 517.1 Mathematical analysis --- 517.1 --- Analyse combinatoire --- Inégalités (mathématiques) --- Fonctions d'une variable réelle --- Mathematical analysis - Problems, exercises, etc --- Mathematiques --- Suites et series --- Problemes et exercices

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An introduction to transform theory

Functional analysis --- Complex analysis --- Integral transforms. --- Integral transforms --- 517.4 --- 517.4 Functional determinants. Integral transforms. Operational calculus --- Functional determinants. Integral transforms. Operational calculus --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Transformations integrales

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This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the previous editions, while updating the context to incorporate recent theoretical and software developments and modern techniques for bifurcation analysis. Reviews of earlier editions: "I know of no other book that so clearly explains the basic phenomena of bifurcation theory." - Math Reviews "The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject." - Bulletin of the AMS "It is both a toolkit and a primer" - UK Nonlinear News.

Bifurcation theory --- Differential geometry. Global analysis --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Bifurcation theory. --- Global analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Differential equations, Nonlinear --- Stability --- Numerical solutions

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This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

Mathematical analysis --- Functions of real variables --- Probabilities --- Real variables --- Mathematical analysis. --- Functions of real variables. --- Probabilities. --- Probability --- Statistical inference --- 517.1 Mathematical analysis --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Functions of complex variables