Why Is Real Analysis Critical in Science and Engineering?

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SUMMARY

Real analysis is critical in science and engineering due to its foundational role in various mathematical branches, including differential geometry, ordinary differential equations (ODEs), partial differential equations (PDEs), probability, and statistics. Key concepts such as limits, continuity, and differentiation are essential for understanding these advanced topics. While some may find Lebesgue integration less appealing, its significance in higher mathematics cannot be overlooked. Overall, real analysis serves as a crucial tool for professionals in mathematics and related fields.

PREREQUISITES
  • Understanding of limits and continuity in calculus
  • Familiarity with differentiation techniques
  • Basic knowledge of differential equations
  • Introduction to probability and statistics
NEXT STEPS
  • Explore the applications of real analysis in differential geometry
  • Study Lebesgue integration and its relevance in probability theory
  • Learn about the role of real analysis in solving ODEs and PDEs
  • Investigate the connections between real analysis and statistical methods
USEFUL FOR

Mathematicians, engineers, and scientists who require a solid understanding of real analysis for advanced studies and practical applications in their fields.

-IamLittle-
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i like limit, continuity,differentiation in real analysis, they are interesting, but i don't know what is their importance?
And about lebesgue integration, i don't think it is interesting, and it seems it is useless
 
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It depends on what you mean by "important". If you mean "useful in other branches of mathematics", then absolutely. If you mean "worth learning because math is an interesting subject for its own sake", then it depends on whether you appreciate mathematics as an art.

If you mean "useful in one's daily life", then probably not, except for a tiny minority of professions.
 
i mean useful in other branches of mathematics
 
Yes; for example, real analysis is of paramount importance in differential geometry, ODEs, PDEs, probability, statistics, and other subfields...
 

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