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A First Course in Mathematical Analysis, by J. C. Burkill
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This straightforward course based on the idea of a limit is intended for students who have acquired a working knowledge of the calculus and are ready for a more systematic treatment which 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. A large number of examples is included, with hints for the solution of many of them.
- Sales Rank: #2551572 in Books
- Color: Green
- Brand: Brand: Cambridge University Press
- Published on: 1978-12-29
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .43" w x 5.43" l, .59 pounds
- Binding: Paperback
- 196 pages
- Used Book in Good Condition
Review
'Books of this quality are rare enough to be hailed enthusiastically ... Essentially an introductory book for the mathematics specialist. But it is so fresh in conception and so lucid in style that it will appeal to anyone who has a general interest in mathematics.' The Times Educational Supplement
'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
' ... it is a pleasure to be able to welcome a book on analysis written by an author who has a sense of style and who avoids the excessive use of symbolism which can make the subject unnecessarily difficult for the student.' Proceedings of the Edinburgh Mathematical Society
Most helpful customer reviews
6 of 6 people found the following review helpful.
A good little "bridge" from School Maths into University
By A Customer
It is amazing that, despite the changing fads in the curriculum, this book has the quality to remain a steadfast bridge from School Mathematics on the first steps into the realm of the Maths specialist for over 40 years now.
The recipe is simple: keep it short, keep it sweet, keep it simple! Mr Burkill has produced a fine little book that gently guides the new student embarking on a specialism in Maths. The author has struck a good balance between the problem solving so familiar at school and introducing the rigour of Mathematical Analysis.
Familiar concepts like differentiation and integration are brought into play right after a quick refresher on numbers and then introducing the notion of limit within the framework of sequences. The delta-epsilon construct is used to great effect to give meaning to the ideas of convergence of sequences and the continuity of functions.
These then lead naturally to the Differential calculus where previously learnt ideas like the rules of differentiation are placed in a rigorous setting and interesting elementary analytical results such as the Mean Value Theorem and Taylor's theorem are discussed. The chapter on Infinite series together with the elementary rules for testing for convergence is followed by a chapter on the special functions of analysis as defined in terms of series - e.g. exp, log, sin, cos, etc.
The chapter on the Integral Calculus makes a natural next step utilising the ideas of an integral as a limit and of infinite series. Specific techniques such as the integral to infinity and approximation methods are placed on a rigorous footing. The final chapter introduces functions of several variables.
The book has lots of worked examples within the text, which aid understanding of new material. As a bonus, there are also several end of section with notes/hints at the end of the book.
Overall, this is a gentle introduction to Analysis and will help anyone who is overawed by the subject on first encounter.
2 of 3 people found the following review helpful.
An ideal first analysis book
By Dave the Math Guy
This book is entirely appropriate as an introduction to analysis for students already familiar with the Calculus. It is on the reading list at Cambridge and Oxford for their undergraduate analysis courses and its reputation is well established. It is not too abstruse but is exceptionally clear and straightforward.
0 of 1 people found the following review helpful.
Very Good Book
By Gaojie Chen
It is my textbook. Very good introductory book for year two university students who have some knowledge about Calculus and Linear algebra.
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