Mathematical Analysis by Apostol

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SUMMARY

The second edition of "Mathematical Analysis" by Apostol significantly differs from the first edition, as confirmed in the preface. Key enhancements include the development of point set topology within metric spaces and Euclidean n-space, the addition of two new chapters on Lebesgue integration, and the removal of content related to line integrals, vector analysis, and surface integrals. The chapter order has been rearranged, with many sections completely rewritten and new exercises introduced. These changes indicate that the second edition offers a more comprehensive and updated approach to mathematical analysis.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with metric spaces
  • Knowledge of Lebesgue integration
  • Experience with mathematical proofs and analysis
NEXT STEPS
  • Explore metric spaces in detail
  • Study Lebesgue integration techniques
  • Review vector analysis and its applications
  • Investigate the structure and content of mathematical textbooks
USEFUL FOR

Students of mathematics, educators teaching analysis, and anyone seeking to deepen their understanding of advanced mathematical concepts and their applications.

Werg22
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Is there a big difference between the 1st and the 2nd edition? I'm considering buying the book, and the 1st edition is much cheaper, but I suspect it may not be that good.
 
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Well, in the preface to the second edition, Apostol writes:

"The second edition differs from the first in many respects. Point set topology is developed in the setting of metric spaces as well as in Euclidean n-space, and two new chapters have been added on Lebesgue integration. The material on line integrals, vector analysis, and surface integrals has been deleted. The order of some chapters has been rearranged, many section having been completely rewritten, and several new excercises have been added."

I have not read the first edition, I've read parts of the second, so I can't comment. I do agree that when a book becomes popular, the price becomes bloated.
 

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