A Course in Real Analysis
Auteur : Junghenn Hugo D.
A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book?s material has been extensively classroom tested in the author?s two-semester undergraduate course on real analysis at The George Washington University.
The first part of the text presents the calculus of functions of one variable. This part covers traditional topics, such as sequences, continuity, differentiability, Riemann integrability, numerical series, and the convergence of sequences and series of functions. It also includes optional sections on Stirling?s formula, functions of bounded variation, Riemann?Stieltjes integration, and other topics.
The second part focuses on functions of several variables. It introduces the topological ideas (such as compact and connected sets) needed to describe analytical properties of multivariable functions. This part also discusses differentiability and integrability of multivariable functions and develops the theory of differential forms on surfaces in Rn.
The third part consists of appendices on set theory and linear algebra as well as solutions to some of the exercises. A full solutions manual offers complete solutions to all exercises for qualifying instructors.
With clear proofs, detailed examples, and numerous exercises, this textbook gives a thorough treatment of the subject. It progresses from single variable to multivariable functions, providing a logical development of material that will prepare students for more advanced analysis-based courses.
Functions of One Variable: The Real Number System. Numerical Sequences. Limits and Continuity on R. Differentiation on R. Riemann Integration on R. Numerical Infinite Series. Sequences and Series of Functions. Functions of Several Variables: Metric Spaces. Differentiation on Rn. Lebesgue Measure on Rn. Lebesgue Integration on Rn. Curves and Surfaces in Rn. Integration on Surfaces. Appendices. Bibliography. Index.
Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics. His research interests include functional analysis, semigroups, and probability.
Date de parution : 04-2015
15.6x23.4 cm
Thèmes d’A Course in Real Analysis :
Mots-clés :
Sin Θ1 Sin Θ2; Dirichlet Function; differential and integral calculus; Lim Inf; undergraduate textbook on real analysis; Vice Versa; functions of one variable; Borel Measurable Functions; functions of several variables; Riemann Integral; compact and connected sets; Lim Supn; analytical properties of multivariable functions; Fubini Tonelli Theorem; differentiability and integrability; Bolzano Weierstrass Theorem; theory of differential forms on surfaces; Continuously Differentiable; axiomatic account of the real number system; Lim Infn; Lebesgue integral; Uniformly Continuous; differentiable manifolds; Lebesgue Measurable; Cauchy Sequence; Improperly Integrable; Borel Sets; Cos Θ1 Sin Θ2; C1 Function; Sequential Characterization; Totally Bounded; Additive Inverse; Cos Θ1 Cos Θ2; Reduced Row Echelon Form; Lebesgue Outer Measure
