A First Course in Mathematical Analysis by David Alexander Brannan (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book pretty much copies the Real Analysis part of the Open University’s excellent course ‘Into to Pure Mathematics’ which also covered Group Theory and Linear Algebra . If you’re new to Analysis I cannot more highly recommend another book, though I would also recommend Spivak’s Calculus which is at the same level, and pretty much covers the same material. I did the course (and have the book) and found it a breeze, all due to the excellently presented material, and the many examples, where like the SUMS books (of which I recommend most), all answers are givern in detail; which is important when you start more advanced maths (sic) and especially when you’re teaching yourself! However it is only an introduction, but will prepare you for more advanced Analysis books like Rudin, Royden and my new favourite Knapp and his 2 Real Analysis books. Personally I wish they would produce more of the OU Maths courses in book format, as the material that I have read and studied has rarely been bettered in the standard books. Maybe this is a start of a new trend with the OU, I hope!

⭐The reviews by Andrew Bigelow and A. Cox are right on the money! I can’t really improve upon what they have written but would add that the fact that the solutions are included at the back of the book make this extremely useful for self study…. I also found the presentation on things like limits far superior to anything I have seen in many recent Calculus textbooks. If you are reading these reviews and are on the fence I wholly recommend you buy it!

⭐This book is a gem.As the author states in the introduction, this is a student friendly book – the notes in the margins are really useful, the worked examples are clear and well thought out while the book has a good flow to it. A lot of thought has been put into this text and it shows. The bottom line is that I learnt a lot from this book and now feel ready to tackle more advanced texts.

⭐I chose this rating because the book was exactly as described. It is a good book and I would recommend to others

⭐As new condition. Spot on as described.

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