Real analysis text book

In summary, there are several recommended textbooks for self-study in real and complex analysis, including "Foundations of Mathematical Analysis" by Pfaffenberger and Johnsonbaugh, "Mathematical Analysis" by Apostol, "Principles of Mathematical Analysis" by Rudin, "Introduction to Analysis" by Arthur Mattuck, and "Visual Complex Analysis" by Tristan Needham. Jean Dieudonne's "Foundations of Modern Analysis" is also highly praised as a reference book, but may be difficult for self-study. Other recommended books include "Analysis I and II" by Lang, "Method of Real Analysis" by Goldberg, "Intro to Real Analysis" by Bartle and Sherbert, and "Elements of Real Analysis"
  • #1
I'm a physics major (undergrad) who wants to learn real and complex analysis, but don't have the time to do the courses in my programme. Can anyone recommend a good textbook for learning the subjects on your own?
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  • #2
good intro books in analysis are:
Foundations of Mathematical Analysis - Pfaffenberger/Johnsonbaugh
Mathematical Analysis - Apostol
Principles of Mathamatical Analysis - Rudin

Foundations of Mathametical Analysis is published by Dover so it will be cheaper than the others. It also has something like 750 problems, and is more 'user friendly' than the others also (imho).

The best book on complex analysis for a physicist would have to be the one by Brown/Churchill. That book rocks
  • #3
Arthur Mattuck's Introduction to Analysis is great and perfect for self-study (I read it on my own). It combines the formality of a regular textbook with informal notes to the reader explaining the stuff that trips up most students. He's an awesome lecturer and his style carries through to the book.

I'm currently reading Tristan Needham's Visual Complex Analysis and it's just outstanding. I've seen some reviews say "This is great, but use it as a secondary book, not as a primary one"; I think that mostly means that you might not have the rigor to ace your Complex Analysis final if you get all your complex analysis from this book. But it's totally self-contained, very clear, and beautiful. I bet there's no better way to really get a feeling for what the subject is all about.
  • #4
It is hard, but a great book is "foundations of modern analysis" by jean dieudonne. mainly for reals. it covers metric spaces, banach and hilbert spaces, real calculus in finite and infinite dimensions, complex analysis, and soime differential equations and sturm liouville theory. this is a great book for reference if not for self study. for years i noticed almost every tricky question i tried to find a proof of occurs as an exercise in this book with hints. there is even a proof of the jordan curve theorem. but no lebesgue integration.

rudin is notoriously difficult to learn from but is the favorite of professional analysts. i do not know if any of them learned from it, but they all seem to like to teach from it.

mattuck is a terrific teacher, and i think his book is a lot more elementary than rudin.

i think i have never seen a bad complex analysis book. my favorite is by cartan.

there was one i think by greenleaf i liked a lot.
  • #5
i agree that dieuodenne is great . aso try lang analysis i and Ii easy to readand comphrensive goldberg book method of real abnalysis bartle and sherbat intro to real analysis bartke (elements of real analysis are all excellent.
but dieuodene lang and cartan all suffer ias they use regulated functions. they failed to acknowledge henstock integral.

What is real analysis?

Real analysis is a branch of mathematics that deals with the study of real numbers and their properties. It is concerned with the rigorous examination of mathematical concepts and their applications in calculus, geometry, and other areas of mathematics.

What topics are typically covered in a real analysis textbook?

A real analysis textbook typically covers topics such as real number systems, sequences and series, continuity, differentiation, integration, and metric spaces.

What are some common applications of real analysis?

Real analysis has various applications in fields such as physics, engineering, economics, and computer science. It is used to study and analyze complex systems and phenomena by providing a rigorous mathematical framework.

What skills are required to understand a real analysis textbook?

A strong foundation in calculus, linear algebra, and mathematical proofs is necessary to understand a real analysis textbook. Familiarity with mathematical notation and logical reasoning is also important.

What are some recommended real analysis textbooks for beginners?

Some recommended real analysis textbooks for beginners include "Principles of Mathematical Analysis" by Walter Rudin, "Real Analysis: A First Course" by Russell Gordon, and "Understanding Analysis" by Stephen Abbott. It is important to choose a textbook that is suitable for one's level of mathematical background and offers clear explanations and examples.

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