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Cover: 9781461264286 | A First Course in Calculus | Serge Lang | Taschenbuch | Paperback
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A First Course in Calculus
Taschenbuch von Serge Lang
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
This is the fifth edition of Lang's caclulus book. It covers all of the topics traditionally taught in the first-year calculus sequence. Each section of A FIRST COURSE IN CALCULUS contains examples and applications of the topic covered. In addition, the back of the book contains detailed solutions to a large number of the exercises. These can be used as worked-out examples, and constitute one of the main changes from previous editions.
Inhaltsverzeichnis
One Review of Basic Material.- I Numbers and Functions.- II Graphs and Curves.- Two Differentiation and Elementary Functions.- III The Derivative.- IV Sine and Cosine.- V The Mean Value Theorem.- VI Sketching Curves.- VII Inverse Functions.- VIII Exponents and Logarithms.- Three Integration.- IX Integration.- X Properties of the Integral.- XI Techniques of Integration.- XII Applications of Integration.- Four Taylor's Formula and Series.- XIII Taylor's Formula.- XIV Series.- Five Functions of Several Variables.- XV Vectors.- XVI Differentiation of Vectors.- XVII Functions of Several Variables.- XVIII The Chain Rule and the Gradient.- Answer.
Details
Erscheinungsjahr: 2012
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: xv
731 S.
20 s/w Illustr.
ISBN-13: 9781461264286
ISBN-10: 1461264286
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lang, Serge
Auflage: 5th ed. 1986. Softcover reprint of the original 5th ed. 1986
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 41 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 13.09.2012
Gewicht: 1,118 kg
Artikel-ID: 106118872
Zusammenfassung
This is the fifth edition of Lang's caclulus book. It covers all of the topics traditionally taught in the first-year calculus sequence. Each section of A FIRST COURSE IN CALCULUS contains examples and applications of the topic covered. In addition, the back of the book contains detailed solutions to a large number of the exercises. These can be used as worked-out examples, and constitute one of the main changes from previous editions.
Inhaltsverzeichnis
One Review of Basic Material.- I Numbers and Functions.- II Graphs and Curves.- Two Differentiation and Elementary Functions.- III The Derivative.- IV Sine and Cosine.- V The Mean Value Theorem.- VI Sketching Curves.- VII Inverse Functions.- VIII Exponents and Logarithms.- Three Integration.- IX Integration.- X Properties of the Integral.- XI Techniques of Integration.- XII Applications of Integration.- Four Taylor's Formula and Series.- XIII Taylor's Formula.- XIV Series.- Five Functions of Several Variables.- XV Vectors.- XVI Differentiation of Vectors.- XVII Functions of Several Variables.- XVIII The Chain Rule and the Gradient.- Answer.
Details
Erscheinungsjahr: 2012
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: xv
731 S.
20 s/w Illustr.
ISBN-13: 9781461264286
ISBN-10: 1461264286
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lang, Serge
Auflage: 5th ed. 1986. Softcover reprint of the original 5th ed. 1986
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 41 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 13.09.2012
Gewicht: 1,118 kg
Artikel-ID: 106118872
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