A Second Course in Mathematical Analysis (Cambridge Mathematical Library) by J. C. Burkill (PDF)

Description

The classic analysis textbook from Burkill and Burkill is now available in the Cambridge Mathematical Library. This straightforward course, based on the idea of a limit, is for students of mathematics and physics who have acquired a working knowledge of calculus and are ready for a more systematic approach. The treatment given here also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series. Particular attention is given to clarity of exposition and the logical development of the subject matter.

User’s Reviews

Editorial Reviews: Review ‘Books of this quality are rare enough to be hailed enthusiastically… it is so fresh in conception and so lucid in style that it will appeal to anyone who has a genuine interest in mathematics.’ The Times Literary Supplement’It is a pleasure to be able to welcome a book on analysis written by an author who has a sense of style.’ Proceedings of the Edinburgh Mathematical Society’This is an excellent book … If I were teaching a course for honours students of the type described, this book would rank high as a possible choice of text.’ Canadian Mathematical Bulletin Book Description A classic calculus text reissued in the Cambridge Mathematical Library. Clear and logical, with many examples.

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

⭐I just need a reference book and have learnt analysis before.Compared to the first course by one of the authors, it seems that the exposition is a lot more verbose…Don’t know if it is suited for a beginner.Maybe an additional author is not necessarily a better thing.Further review: Actually you can use C10-13 to learn complex analysis and C5 (well, maybe not Urysohn’s Lemma)a nd 7 as part of the analysis II material. Other chapters (especially C6), is unnecessarily complex. Plus, you don’t really want to spend so much time on Riemann integrability don’t you…

⭐This book is a truly jewel of analysis, the best book I have found so far in analysis, not for nothing it is the one used for the real analysis course dictated at my University and is the one more asked by mathematics students from the Astronomy, Physics & Mathematics library here also (Pontificia Catholic University of Chile). It has 14 chapters, of which I have only studied the first 9 with exception of chapter 8. In general, I haven’t done the exercises but just a few, my approach with books is like peeling an onion on a first reading just read and understand what’s being said, on a second reading try the exercises (in this way you can go as quick as you can on covering the material) etc. Also about the exercises I MUST point out that the majority come with answers at the back of the book! I found this awesome and specially suited for self study (which is my case, by the way).The writing is very clear, beautiful and complete. I specially like chapters 1 to 3 where the main concepts addressed are sets, metric spaces, functions and point set topology, chapter 7 where everything related to the concept of the linear derivative for functions of arbitrary domain and range (e.g. f:Rm x Rn–>Rp) are deal with paving the way for the all importants Implicit and Inverse theorem. Chapter 9 (the one I’m currently working on) is about Fourier Series and I must say that I have not found in anywhere else such a complete treatment about Fourier Series and I’m very pleased about this situation.Finally I must tell you that I also have on mathematical analysis the books of T.Apostol, W.Rudin, Courant-John and this is by far the better so if you are thinking about this title my advice is buy it because you will be getting one of those book whose weight is worth on gold, that is, a terrific jewel of analysis.

⭐Very useful

⭐Good product, in good state and shape, received promptly.

⭐This is the second volume ot the authors little book “A first course in mathematical analysis”. This volume is a well written and rigorous exposition of the study of functions in several variables. Differentiation , integration and all. Very good reference book.

⭐Although it’s said that this is used. It’s amazingly new no notes on it and no damage. Great

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