Advanced Calculus

Basically as the title says, I use it for reference when I want to understand a concept better most often in applied applications that are not directly related to this. I often forget some detail that another author leaves out and expects you to fill in, as is often the case in later classes. This is a good book to fill in a lot gaps and because I have some familiarity with this book, I can quickly go through it to find the important detail and then move on. For what I use it for it is 5 stars. Great reference book!

OK. There I was in my sophomore year of college taking Quantum Mechanics 101. Trouble was, I was taking linear algebra that semester, and hadn't had second year calculus let alone differential equations. Meanwhile, my QM book was remarkably... uh... concise. By very happy accident, I found Taylor's book in the school library, and I clung to it for dear life throughout the QM course. Folks, it was wonderful! I could crack this thing in the middle and understand what the man was saying! Some explanations were so clear I wept! (My Gosh! THAT'S why angular momentum couples!) Because of this eminently crack-openable quality, I still have the book as a reference thirty-some-odd years later. There were only two minor disappointments. You see, I actually sent Angus Taylor a fan letter, at UCLA. Dr. Taylor was kind enough to write me back personally to... plug his other texts... Oh well! We all haveta make a buck, right? Then the next year, I took second year Calculus, and my school switched to this text. I found it so wordy, I wound up using a much shorter text and keeping Ol' Angus as a reference. So, IMHO it didn't work, like, all that well as a text, but as a reference it can't be beat. It is in this role that I recommend it. What use is all that studying, after all, if you cannot recall the material after a few decades?

This book has a clarity unparalleled among books covering similar topics. While it contains an extensive amount of prose, it is still fairly compact: the book explains each result, the motivation for it, and points out possible pitfalls and considerations. Examples are well-chosen, proofs are easily followed. The order of the book is a bit chaotic, but it's written in such a way that it is easy to skip around in it. My only complaint about this book is that I wish it covered a bit more material. This book might not go quite as far as some people might want, especially for a two-semester sequence or for courses at the graduate level. I would recommend this book to anyone who already knows calculus and wants to learn (the more rigorous topic of) analysis on their own, or anyone selecting a textbook for an undergraduate advanced calculus course. This book also makes a good reference, and I was happy to permanently add it to my collection. For a more advanced book covering topics beyond those covered in this book, I would recommend Apostol's analysis book.

I am no expert in the area of Mathematical Analysis, but I am an avid reader of any book that pertains the subject. I found this book in my schools mathematics lounge and could not resist reading it from cover to cover. This book is of the quality of such authors as Buck, Widder, Courant, and Rudin. As another reviewer has noted, this book is definitely worth every penny. It is not dry or to pedantic as some of the other afore mentioned authors, yet it is not simple and lacking in content. Of course like any quality Advanced Calculus book it requires the reader to have mathematical maturity as well as patience and the drive to self-explore the concepts. If one cannot follow simple examples and from those examples formulate their own, they may want to review the very basics of mathematics or consider a different major. I would highly recommend this book to advanced undergraduates or beginning gradutes students as a reference book or for self study.

This is the advanced calculus text I used at University of Washington while getting my BS in mathematics. I loved it then, and I've just purchased another copy to use for review. It's extremely well written. If you're looking for a good second year calculus text, this one's it.