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681 kr
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We learn by doing. We learn mathematics by doing problems. And we learn more mathematics by doing more problems. This is the sequel to ""Problems in Mathematical Analysis I"" (Volume 4 in the ""Student Mathematical Library"" series). If you want to hone your understanding of continuous and differentiable functions, this book contains hundreds of problems to help you do so. The emphasis here is on real functions of a single variable. The topics include: continuous functions, the intermediate value property, uniform continuity, mean value theorems, Taylors formula, convex functions, sequences and series of functions. The book is mainly geared toward students studying the basic principles of analysis.However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of the material is designed to help student comprehension, to encourage them to ask their own questions, and to start research. The collection of problems will also help teachers who wish to incorporate problems into their lectures. The problems are grouped into sections according to the methods of solution. Solutions for the problems are provided. This is the sequel to ""Problems in Mathematical Analysis I"" (Volume 4 in the ""Student Mathematical Library"" series). Also available from the AMS is ""Problems in Analysis III"".
681 kr
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The best way to penetrate the subtleties of the theory of integration is by solving problems. This book, like its two predecessors, is a wonderful source of interesting and challenging problems. As a resource, it is unequaled. It offers a much richer selection than is found in any current textbook. Moreover, the book includes a complete set of solutions. This is the third volume of ""Problems in Mathematical Analysis"". The topic here is integration for real functions of one real variable.The first chapter is devoted to the Riemann and the Riemann-Stieltjes integrals. Chapter 2 deals with Lebesgue measure and integration. The authors include some famous, and some not so famous, inequalities related to Riemann integration. Many of the problems for Lebesgue integration concern convergence theorems and the interchange of limits and integrals. The book closes with a section on Fourier series, with a concentration on Fourier coefficients of functions from particular classes and on basic theorems for convergence of Fourier series.The book is mainly geared toward students studying the basic principles of analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of the material is designed to help student comprehension, to encourage them to ask their own questions, and to start research. The collection of problems will also help teachers who wish to incorporate problems into their lectures. The problems are grouped into sections according to the methods of solution. Solutions for the problems are provided. ""Problems in Mathematical Analysis I and II"" are available as Volumes 4 and 12 in the AMS series, ""Student Mathematical Library"".