Book Titles Analysis I

Hardcover		Analysis I Claus Gerhardt, University of Heidelberg, Germany
		ISBN-10: 1-57146-153-1 ISBN-13: 978-1-57146-153-7 Year Published: 2004 Pages: 281 pp. Binding: Hardcover Price: $65.00

Description: This is the first part of an introduction to analysis in two volumes based on the author's undergraduate courses, Analysis I -- III, and the more advanced course, Tensor Analysis, at Heidelberg. The contents of both volumes range from elementary calculus to fairly advanced topics in functional analysis, measure theory and differential geometry. The first volume, Analysis I, covers some fundamental concepts of logic, set theory and the real numbers, the convergence of sequences and series in the real line, Euclidean spaces as well as Banach spaces, topological concepts including continuity, compactness and connectedness, differentiation in one variable, the theorems of Arzela-Ascoli and Stone-Weierstraß and analytic functions in several variables, as well as the Riemann integral. The present book can be used as a textbook, it comprises of materials for a one and a half semester course. The book, which demands minimum prerequisites, is intended as a textbook for first year graduate students or for undergraduates who later want to graduate in Mathematics or Physics. Table of Contents (chapters): View Preface and Table of Contents as PDF file Chapter 0: Foundations (Elements of Logic, Elements of set theory, Cartesian Product, Functions and Relations, Natural and Real Numbers) Convergence (Convergence in R, Infinite series in R, Convergence in Rn, Metric spaces, Series in Banach spaces, Uniform convergence, Complex numbers) Continuity (Topological concepts, Continuous maps, Compactness, The Tietze-Urysohn extension theorem, Connectedness, Product spaces, Continuous linear maps, Semicontinuous functions) Differentiation in one Variable (Differentiable functions, The mean value theorem and its consequences, De L'Hospital's Rule, Differentiation of sequences of functions, The differential equation x' = Ax, The elementary functions, Polynomials, Taylor's formula) Spaces of continuous functions (Dini's theorem, Arzela-Ascoli Theorem, The Stone-Weierstraß Theorem, Analytic functions) Integration in one variable (The Riemann integral, Integration rules, Monotone and continuous functions are integrable, Fundamental theorem of calculus, Integral theorems and transformation rules, Integration of rational functions, Lebesgue's integrability criterion, Improper integrals, Parameter dependent integrals) Related Books: Analysis II, Claus Gerhardt - * SPECIAL: Buy Analysis I and Analysis II and receive a 10% discount! To Order: Book Orders Book Sales - Great discounts on other popular titles!