Mathematical analysis
著者
書誌事項
Mathematical analysis
（Universitext）
Springer, c2008-2010
- 1
- 2
- タイトル別名
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Anailisi matematica
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注記
"Translated from the original Italian edition: C. Canuto, A. Tabacco: Analisi matematica II, Springer-Verlag Italia, Milano, c2008"--T.p. verso of 2
Includes index
内容説明・目次
- 巻冊次
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1 ISBN 9788847008755
内容説明
The recen t Europea n Programm e Specification s hav e force d a reassessmen t o f th e structure an d syllab i o f th e entir e syste m o f Italia n highe r education , an d a n ensuing rethinkin g o f th e teachin g material . Nowadays man y lectur e courses , especiall y rudimentar y ones , deman d tha t st- dents maste r a larg e amoun t o f theoretica l an d practica l knowledg e i n a spa n o f just fe w weeks , i n orde r t o gai n a smal l numbe r o f credits . A s a result , instructor s face th e dilemm a o f ho w t o presen t th e subjec t matter . The y mus t mak e appr- priate choice s abou t lectur e content , th e comprehensio n leve l require d fro m th e recipients, an d whic h kin d o f languag e t o use .
目次
Basic notions.- Functions.- Limits and continuity I.- Limits and continuity II.- Local comparison of functions. Numerical sequences and series.- Differential calculus.- Taylor expansions and applications.- Geometry in the plane and in space.- Integral calculus I.- Integral calculus II.- Ordinary differential equations.
- 巻冊次
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2 ISBN 9788847017832
内容説明
The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort "Mathematical Analysis I". The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities. While the subject matter known as 'Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on 'Calculus 2' can vary a lot, resulting in a bigger flexibility. For these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is not comparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book. On the website, the interested reader may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material.
The Authors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the student put his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined.
目次
Numerical series.- Series of functions and power series.- Fourier series.- Functions between Euclidean spaces.- Differential calculus for scalar functions.- Differential calculus for vector-valued functions.- Applying differential calculus.- Integral calculus in several variables.- Integral calculus on curves and surfaces.- Ordinary differential equations.
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