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I am looking for analysis books that can explain thing clearly and contain many good examples to help me understand the math.

I don't possess a very in-depth knowledge of mathematics. Also, it's alright if the book is quite lengthy or pricey.

Lord_Farin
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Matsumoto Yoshiharu
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    What is "little knowledge"? Do you want the book to be in Japanese or is English okay? – Lemon Jun 15 '13 at 06:49
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    Welcome to MSE! Do you have a specific math area for the analysis books? Regards – Amzoti Jun 15 '13 at 06:49
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    Tell us a little bit about your background – user42912 Jun 15 '13 at 06:49
  • In Russian there is a classical book by G. M. Fichtenholz «A Course of Differential and Integral Calculus» in three huge volumes with a lot of examples. Unfortunately, I don’t know are there English or Japanese translations of this book. – Alex Ravsky Jun 15 '13 at 08:40

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This should be a comment, but I can't comment because I don't have enough rep... sorry.

I liked Stephen Lay's Analysis: With an Introduction to Proof (4th Edition) for an easy, slow, example-ridden intro to analysis. It'll work for you if you've taken first year calculus.

Samuel Reid
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This is too long for a comment. My favourite introductory analysis book is Understanding Analysis by Stephen Abbot. It is a great exposition, and highly accessible (I think) to any undergraduate, who has seen a semester of calculus.

One particular feature of this book that I really like (which I also see especially useful for beginners, including me) is how the exercises are intertwined with the main text (most of which have hints and partial solutions). In this way, exercises do not seem insurmountable, but rather as natural continuation of thought from the ideas that immediately precedes the exercise. It is different from the traditional approach, where exercises are all appended to the end of the section, where the student will be expected to conquer them :)

And yes, as far as I remember, this book does have good amount of examples, with the main goal of understanding (real) analysis (hence the name of the book). After/before giving rigorous proof, you will actually see most proofs "dissected" for you, in mathematical sense.

Prism
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