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About this book
The purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica tions which accompany them. The very talented students, with an ob vious aptitude for mathematics, will rapidly require a course in functions of one real variable, more or less as it is understood by professional is not primarily addressed to them (although mathematicians. This book I hope they will be able to acquire from it a good introduction at an early age). I have not written this course in the style I would use for an advanced monograph, on sophisticated topics. One writes an advanced monograph for oneself, because one wants to give permanent form to one's vision of some beautiful part of mathematics, not otherwise ac cessible, somewhat in the manner of a composer setting down his sym phony in musical notation. This book is written for the students to give them an immediate, and pleasant, access to the subject. I hope that I have struck a proper com promise, between dwelling too much on special details and not giving enough technical exercises, necessary to acquire the desired familiarity with the subject. In any case, certain routine habits of sophisticated mathematicians are unsuitable for a first course. Rigor. This does not mean that so-called rigor has to be abandoned.
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Table of contents (18 chapters)
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Front Matter
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Review of Basic Material
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Front Matter
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Differentiation and Elementary Functions
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Front Matter
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Integration
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Front Matter
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Taylor’s Formula and Series
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Front Matter
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Functions of Several Variables
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Front Matter
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Authors and Affiliations
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Bibliographic Information
Book Title: A First Course in Calculus
Authors: Serge Lang
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-8532-3
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1986
Hardcover ISBN: 978-0-387-96201-6Published: 15 January 1986
Softcover ISBN: 978-1-4612-6428-6Published: 13 September 2012
eBook ISBN: 978-1-4419-8532-3Published: 17 September 2012
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 5
Number of Pages: XV, 731
Additional Information: Originally published by Addison-Wesley Publishing Company, 1978, 1973, 1968, 1964
Topics: Real Functions