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Guide to Analysis written by Mary Hart
This volume is written specifically for students meeting analysis for the first time. It is designed so that it can be used as a textbook in conjunction with a lecture course in analysis or it can be used by students wishing to teach themselves the subject-independent of any lecture course. For this reason numerous worked examples are included with very detailed solutions to enable the reader to check that the concepts and definitions are understood.
When working the exercises the reader is given the opportunity to receive a little help (or inspiration!) without being given the answer, as the answers and the hints for solutions are recorded in separate sections. In practice, one exercise successfully completed by the reader (even with the help of a few hints) can teach more than several examples read from the text.
Analysis traditionally contains numerous theorems and proofs. These theorems are the tools of the trade and we cannot just dispense with large numbers of them in order either to cut down the size of the volume or to make the learning process appear easier. Neither can we simply omit their proofs. Before using a result we must know for certain that it is true. The need for proof is something which has always been recognised to a greater or lesser extent. Historical records show that the ancient Greek mathematicians living centuries before Christ acknowledged this, and, indeed, some of our presentday proofs, like the contradiction argument, stem from their work. However, the use of the link between limits of functions and sequences allows us a few economies and reduces the number of separate proofs necessary.
Book Detail :-
Title: Guide to Analysis
Author(s): F. Mary Hart
Publisher: Macmillan Education UK
Series: Macmillan Mathematical Guides
ISBN: 978-0-333-43788-9, 978-1-349-09390-8
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About Author :-
Author , Department of Pure Mathematics, University of Sheffield, Sheffield, South Yorkshire, England
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Book Contents :-
Guide to Analysis written by Mary Hart cover the following topics.
1. NUMBERS AND NUMBER SYSTEMS
3. INFINITE SERIES
4. FUNCTIONS Limits of functions, continuous functions
5. DIFFERENTIABLE FUNCTIONS Dilferentiable functions, Rolle's theorem, mean value theorem, Taylor's theorem, I'Hopital's rule, maxima and minima, Taylor series
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