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Review
'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
Product Description
This is a text-book of mathematical analysis. Read the first page
Concordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews
The recipe is simple: keep it short, keep it sweet, keep it simple! The author 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 an introduction to the notion of limit within the framework of sequences. The delta-epsilon construct is used 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 problems accompanied by 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.
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.
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