[Math] Good undergraduate complex analysis textbook

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I'm looking for a textbook aimed at undergraduate students (i.e. a first exposition of complex analysis) but not geared towards applications as Churchill and, if possible, assuming the mathematical maturity a real analysis and an abstract algebra undergrad courses give but not much more (i.e. not extremely terse). Which book is suited for me? I've heard Ahlfors and Conway are good, but aren't those grad-level courses?

Oh, I almost forgot, this is for self-studying so intuition and some examples are appreciated.

Thanks very much in advance!

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Complex Analysis / Edition 1 by THEODORE GAMELIN is very intuitive, and teaches you not only the theory, but also the execution.

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[Math] Expository articles on Analysis and Probability theory

I think that these notes by John Erdmann might satisfy your requirements for at least a portion of the analysis material. First, there is:

A Problem Text in Advanced Calculus

This set of notes covers basis aspects of topology, basic aspects of integral/differential calculus and concludes with the inverse and implicit function theorems.

There is also:

A Companion to Real Analysis

These notes could perhaps be considered as a continuation of his problem text. More topology is discussed, Lebesgue integration, Banach/Hilbert spaces and concludes with some operator theory. There is also some probability thrown in for good measure, pun intended.

For multivariable analysis/calculus, I also like Jerry Shurman's notes that you can find here. He covers some of the same ground that Erdman does, but goes much farther into "vector calculus" including differential forms and Stokes/Gauss' theorems. Like Erdman's, these notes are also extremely well-written.

Also, speaking of professors named Conrad, you might want to look at Brian Conrad's notes on differential geometry found here. Although these notes cover more DG than you may be interested in, he gives a full accounting of Stokes' theorem and the algebra/analysis that is required to get there. The treatment is considerably deeper than that found in Shurman's notes. Each topic is contained in a separate document and there are probably about 50 or so of these documents, usually between 10 and 20 pages apiece.

[Math] Suggestions on Real, Fourier Analysis textbooks

I'd definitely recommend baby Rudin for general introductory analysis, his followup textbook is also my favourite analysis book. Fourier analysis is generally very reliant on Lebesgue integration. A book which uses only the Riemann integral (if I recall correctly) is Dietmar's first.

The route I took into harmonic analysis was starting with A (Terse) Introduction to Lebesgue Integration by Franks, which has an online draft here, which introduces the Lebesgue measure/integral in a very rigorous manner before establishing the basic $L^{2}$ treatment of Fourier series on $\Bbb{T}$. After that, the best recommendation that most people interested in harmonic analysis should read is katznelson's book, which covers the standard Fourier transform on $\Bbb{R}$ material very nicely, as well as sketching the locally compact abelian group stuff. From there, there seems to be less of a general consensus. I found Rudin's Fourier Analysis on Groups excellent for the locally compact abelian case, giving nice proofs of several theorems for which I wasn't happy with the proofs given in other books. I also enjoyed Classical Harmonic Analysis and Locally Compact Groups by Reiter and Stegeman as more of a broad introduction to abelian harmonic analysis, although it does ommit quite a few key proofs. I can't offer many references beyond the abelian case, and certainly not beyond the compact case, but the second of Deitmar's books was my favourite general reference for introductory nonabelian harmonic analysis. I've not read much of it, but my favourite treatment of the compact case is that found in Folland's book, which is online here; in particular, I found that its description of the representation theory was much more natural than other treatments.

I'm not American, so I can't relate what I've said to the courses you've listed, but hopefully this will help somewhat. I'd certainly recommend starting with Franks and Katznelson.

As a general aside related to your comments, I'd recommend trying to read as much as possible without asking for help from your professors - even if you ultimately have to ask for some help understanding something, you'll get much, much more from it if you only ask for help once you've beaten your brains out trying to understand it.

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[Math] Expository articles on Analysis and Probability theory

[Math] Suggestions on Real, Fourier Analysis textbooks

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