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This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces.
Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references.
Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis.
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Sequences and Limits
Series of Functions
Approximation by Polynomials
Various Proof ?(2) = ?2/6
Functions of Several Variables
Prime Number Theorem
Readership: Undergraduates and graduate students in mathematical analysis.
A comprehensive collection of important and instructive problems in real analysis together with their detailed solutions
Many solutions are accessible to undergraduate students taking courses in calculus and linear algebra
Many problems related to analytic number theory, including Prime Number Theorem, are provided