What differentiates Advanced Calculus from Real Analysis?

In summary: If you're interested in diving into more abstract topics, then Real Analysis would be a better fit for you.
  • #1
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,584
24
Has anyone ever seen this? It's an interactive online textbook in analysis in a single real variable. As an undergrad, I wussed out and took Advanced Calculus instead of Analysis, and this is a subject I've been meaning to learn. Is anyone interested in going through this?

http://www.shu.edu/projects/reals [Broken]

It looks like it could serve as a springboard to get into more advanced books that I've found online.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
This will seem like a really silly question but...

As long as we're sticking to real functions of a single variable (and not delving into abstract spaces and measures), what's the difference? (I'm beginning to suspect that my teacher taught us both in my advanced calc courses)
 
  • #3
i think "analysis" has to have the word "real" in front to be compared to advanced calculus.

otherwise, things like metric spaces are included in the subject.
 
  • #4
To a mathematician, the word analysis by itself means functions of a complex variable. Other discplines mean other things by it. The Freudians...
 
  • #5
I talked with a coworker, and he confirmed my suspicions; my advanced calc class did indeed delve a decent bit into real analysis, which is the source of my confusion!
 
  • #6
An (almost) pure PF Mentor page!
 
  • #7
i think the term "function theory" is what is used for complex analysis.

not all mathematicians have the same definition of "analysis."

http://mathworld.wolfram.com/Analysis.html

Originally posted by selfAdjoint
To a mathematician, the word analysis by itself means functions of a complex variable. Other discplines mean other things by it. The Freudians...
 
  • #8
Originally posted by Hurkyl
As long as we're sticking to real functions of a single variable (and not delving into abstract spaces and measures), what's the difference? (I'm beginning to suspect that my teacher taught us both in my advanced calc courses)

OK, sorry I took so long to get back to you. As far as I know, the thing that differentiates Advanced Calculus from Real Analysis is theorem proving. In my Adv Calc class, we covered multivariable calculus (differential and integral), vector calculus, calculus of variations, and a very little bit of PDEs. We learned nothing of spaces, measures, Lebesgue integration, etc.
 

1. What is instructive real analysis?

Instructive real analysis is a branch of mathematics that deals with the study of real numbers and their properties. It focuses on understanding the behavior and relationships between real numbers, as well as the concepts of limits, continuity, derivatives, and integrals.

2. What are the main topics covered in instructive real analysis?

The main topics covered in instructive real analysis include basic set theory, functions and their properties, sequences and series, limits and continuity, derivatives, integrals, and applications of these concepts to real-world problems.

3. How is instructive real analysis different from other branches of mathematics?

Unlike other branches of mathematics, instructive real analysis is specifically focused on the study of real numbers and their properties. It also places a strong emphasis on proofs and rigorous mathematical reasoning.

4. What are the applications of instructive real analysis?

Instructive real analysis has a wide range of applications in fields such as physics, engineering, economics, and computer science. It is particularly useful in understanding and solving problems involving rates of change, optimization, and measurement.

5. What are some common difficulties students face when learning instructive real analysis?

Some common difficulties students face when learning instructive real analysis include grasping abstract concepts, understanding and constructing rigorous proofs, and applying mathematical concepts to real-world problems.

Similar threads

  • Calculus
Replies
0
Views
1K
Replies
8
Views
2K
  • Science and Math Textbooks
Replies
13
Views
2K
  • Science and Math Textbooks
Replies
4
Views
2K
  • Science and Math Textbooks
Replies
24
Views
3K
Replies
13
Views
2K
Replies
1
Views
1K
  • STEM Academic Advising
Replies
9
Views
1K
Back
Top