Exploring the Differences between Advanced Calculus and Introduction to Analysis

[Nusc]

Some institutions regard the two as the same and some do not. I'm curious to know what exactly the difference are between the two are.

I speak of the second/third year advanced calculus and introduction to analysis course.

Some instutions use less rigorous texts and some use Rudin.

I can't really distinguish between the two and would like speculation.

Thanks

 

[gravenewworld]

It depends on the school. Read the course description guide. At my school Advanced calc=real analysis. We used Intro. to Real Analysis by Michael Reed for our course. It all starts w/ the rigorous definition of a limit and then you apply it to derivatives and then go to integrals.

 

[HallsofIvy]

Engineering schools, in particular, tend to regard "Advanced Calculus" as exactly that: More advance version of the same calculus you've been having including some applications like numerical analysis, differential equations, special functions.

Large colleges that have BOTH "Advanced Calculus" and "Analysis" courses may do something similar with analysis being purely theoretical calculus.
Smaller colleges that do not have strong engineering schools, so that it is mostly math majors taking it, tend to do "Advanced Calculus" as an intrductory analysis course.

 

[Manchot]

Interestingly enough, my university math department's Advanced Calculus class is actually a vector calculus class.

 

[Eratosthenes]

Depends on the school as the others have said. At my school Advanced Calculus is an intro to analysis course. Although currently we are studying things in R^n, convergence, compact sets, continuity, connected sets, metric spaces, etc. This is what is typically covered in an intro to analysis II course, so it depends on who the professor is also. The material is fascinating but difficult. If you are a math major, I would think it's essential to master this material. My prof. always emphasizes it is good knowledge to have for graduate school.