Problems and Solutions for Undergraduate Analysis

Problems and Solutions for Undergraduate Analysis (Undergraduate Texts in Mathematics)

The present volume contains all the exercises and their solutions for Lang's second edition of Undergraduate Analysis. The wide variety of exercises, which range from computational to more conceptual and which are of varyÂ ing difficulty, cover the following subjects and more: real numbers, limits, continuous functions, differentiation and elementary integration, normed vector spaces, compactness, series, integration in one variable, improper integrals, convolutions, Fourier series and the Fourier integral, functions in n-space, derivatives in vector spaces, the inverse and implicit mapping theorem, ordinary differential equations, multiple integrals, and differential forms. My objective is to offer those learning and teaching analysis at the undergraduate level a large number of completed exercises and I hope that this book, which contains over 600 exercises covering the topics mentioned above, will achieve my goal. The exercises are an integral part of Lang's book and I encourage the reader to work through all of them. In some cases, the problems in the beginning chapters are used in later ones, for example, in Chapter IV when one constructs-bump functions, which are used to smooth out singulariÂ ties, and prove that the space of functions is dense in the space of reguÂ lated maps. The numbering of the problems is as follows. Exercise IX. 5. 7 indicates Exercise 7, Â§5, of Chapter IX. Acknowledgments I am grateful to Serge Lang for his help and enthusiasm in this project, as well as for teaching me mathematics (and much more) with so much generosity and patience.
Country USA
Brand Springer
Manufacturer Springer
Binding Paperback
ItemPartNumber 9780387982359
UnitCount 1
EANs 9780387982359
ReleaseDate 0000-00-00

Country	USA
Brand	Springer
Manufacturer	Springer
Binding	Paperback
ItemPartNumber	9780387982359
UnitCount	1
EANs	9780387982359
ReleaseDate	0000-00-00

Problems and Solutions for Undergraduate Analysis (Undergraduate Texts in Mathematics)

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