A First Course in Mathematical Analysis

by David Alexander Brannan

Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.

Genres: Mathematics

459 pages, Paperback

First published July 1, 2006

Reviews

[Craine · Rating 5 out of 5]

Having worked with several books in real analysis this book is by far the most approachable textbook to get if you are interested in real analysis. This goes double if you are coming from a different background than mathematics such as economics where the design of the book mimics more the aesthetics of science related books than that of math. One may think that this remains a superficial observation, but it does indeed serve a deeper purpose as it helps people from related disciplines easier approach the subject by feeling less intimidated by set up off the book which avoids the typical theorem-proof minimal explanations that you often see in proof based books. It also helps that the book uses prose that is easily digestible as well as offering up exercises for each section. I did loads of exercises from the book and can attest that they range around the expected slightly easier problems that you find in other books. All the more reason to pick this book up if you are a beginner to the subject. Anyways, haven given this book enough praise, I highly recommend picking it up as a first real analysis book. For those more experienced with the material you can always jump to baby Rudin.

Note: I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system increases in my humble opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars of a given book.)

[szymborskalyte · Rating 5 out of 5]

Excellent primer for analysis, even for someone with relatively weak mathematical facility.

[Darin · Rating 4 out of 5]

This book emphasizes basic details that are probably assumed known in many analysis courses. Someone at the graduate level (who understands the material at that level) would find this book to be too simple, but I found it to be very helpful while taking an undergraduate analysis course.

Note that I believe (and follow) the meanings Goodreads gives for what each number of stars means. Therefore, the majority of my ratings are 3 stars ("liked it").

[Mariano Apuya · Rating 4 out of 5]

I am trying to read textbooks. And I have a preselected list. When I got Brannan's book I just set all the planned reading I have and just work on this textbook. It is a great textbook, It was designed for self study and he succeeds in this at all levels. I am currently on section 1.3 on inequalities and so far I am keeping up. I find that I enjoy studying it.