Why Is Real Analysis Critical in Science and Engineering?

[-IamLittle-]

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

 

[uman]

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.

 

[-IamLittle-]

i mean useful in other branches of mathematics

 

[uman]

Yes; for example, real analysis is of paramount importance in differential geometry, ODEs, PDEs, probability, statistics, and other subfields...