Advanced Calculus/Real Analysis Book

[tarheelborn]

I am currently taking an advanced calculus course and, for the most part, I really like it. However, I believe I could benefit from a supplemental textbook. My class uses Goldberg's Methods of Real Analysis. I would like to be able to find a text that offers more detailed explanations and, particularly, step-by-step examples to show the theorems. I suppose I need a "for dummies" version of advanced calculus. I am an older student, attempting to refresh/learn enough to get into graduate school in mathematics. Thanks for your help.

[jbunniii]

I recommend

Elementary Real Analysis (http://www.amazon.com/Elementary-Real-Analysis-Brian-Thomson/dp/143484367X/) by Thomson, Bruckner, and Bruckner.

You can preview parts of it using the "look inside" feature at Amazon to see if it's what you are after. The price is pretty good at $27 for a paperback, or you can download a full PDF version here for a token charge (I think it was literally one dollar, with substantial chunks available for free):

Classical Real Analysis (http://classicalrealanalysis.com/TBB.aspx)

Caution: the same authors also published a graduate-level book called "Real Analysis."

[tarheelborn]

Thank you so much!

[Reedeegi]

Two books published by Dover that are, in my opinion, excellent for your purpose are

Elementary Real and Complex Analysis (http://www.amazon.com/Elementary-Complex-Analysis-Dover-Mathematics/dp/0486689220/ref=sr_1_1?ie=UTF8&s=books&qid=1255201897&sr=1-1) by Georgi Shilov

and
Introduction to Analysis (http://www.amazon.com/Introduction-Analysis-Maxwell-Rosenlicht/dp/0486650383/ref=pd_sim_b_5) by Maxwell Rosenslicht.

Also, if you plan on pursuing pure math, Dover is a fantastic publisher offering many cheap, well-written texts that are far better than many texts put out by publishers for 5-10x the price. To see their math catalogue, go to this webpage (http://store.doverpublications.com/by-subject-science-and-mathematics-mathematics.html).

Best of luck!

[n!kofeyn]

Analysis: With an Introduction to Proof by Steven Lay
This book is an excellent starter to analysis. It gives many proofs that are extremely clear, and has quite a big chunk devoted to techniques of proof.

Elementary Analysis: The Theory of Calculus by Kenneth Ross

These are great introductory books that don't have an ego.

[tarheelborn]

Thanks for all your help!