Short Calculus: The Original Edition of "A First Course in Calculus" by Serge La

Description: Short Calculus by Serge Lang This is a reprint of the original edition of Langs classic book "A First Course in Calculus". It covers all of the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description Praise for the first edition:"..Langs present book is a source of interesting ideas and brilliant techniques." Acta Scientiarum Mathematicarum"..It is an admirable straightforward introduction to calculus." MathematikaThis is a reprint of A First Course in Calculus, which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students background was not as substantial as it might be. We are now back to those times, so its time to start over again.There are no epsilons-delta, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950. Notes This is a reprint of the original edition of Langs classic book "A First Course in Calculus". It covers all of the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. The audience consists of those taking the first calculus course, in high school or college. "..Langs present book is a source of interesting ideas and brilliant techniques." Acta Scientiarum Mathematicarum. "..It is an admirable straightforward introduction to calculus." Mathematika. Back Cover This is a reprint of "A First Course in Calculus," which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the studentsbackground was not as substantial as it might be. We are now back to those times, so its time to start over again. There are no epsilon-deltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950. Table of Contents I Numbers and Functions.- 1. Integers, rational numbers and real numbers.- 2. Inequalities.- 3. Functions.- 4. Powers.- II Graphs and Curves.- l. Coordinates.- 2. Graphs.- 3. The straight line.- 4. Distance between two points.- 5. Curves and equations.- 6. The circle.- 7. The parabola. Changes of coordinates.- 8. The hyperbola.- III The Derivative.- l. The slope of a curve.- 2. The derivative.- 3. Limits.- 4. Powers.- 5. Sums, products, and quotients.- 6. The chain rule.- 7. Rate of change.- IV Sine and Cosine.- l. The sine and cosine functions.- 2. The graphs.- 3. Addition formula.- 4. The derivatives.- 5. Two basic limits.- V The Mean Value Theorem.- 1. The maximum and minimum theorem.- 2. Existence of maxima and minima.- 3. The mean value theorem.- 4. Increasing and decreasing functions.- VI Sketching Curves.- 1. Behavior as x becomes very large.- 2. Curve sketching.- 3. Pol ar coordinates.- 4. Parametric curves.- VII Inverse Functions.- 1. Definition of inverse functions.- 2. Derivative of inverse functions.- 3. The arcsine.- 4. The arctangent.- VIII Exponents and Logarithms.- 1. The logarithm.- 2. The exponential function.- 3. The general exponential function.- 4. Order of magnitude.- 5. Some applications.- IX Integration.- 1. The indefinite integral.- 2. Continuous functions.- 3. Area.- 4. Upper and lower sums.- 5. The fundamental theorem.- 6. The basic properties.- X Properties of the Integral.- 1. Further connection with the derivative.- 2. Sums.- 3. Inequalities.- 4. Improper integrals.- XI Techniques of Integration.- 1. Substitution.- 2. Integration by parts.- 3. Trigonometric integrals.- 4. Partial fractions.- XII Some Substantial Exercises.- 1. An estimate for (n!)1/n.- 2. Stirlings formula.- 3. Wallis product.- XIII Applications of Integration.- 1.Length of curves.- 2. Area in polar coordinates.- 3. Volumes of revolution.- 4. Work.- 5. Moments.- XIV Taylors Formula.- 1. Taylors formula.- 2. Estimate for the remainder.- 3. Trigonometric functions.- 4. Exponential function.- 5. Logarithm.- 6. The arctangent.- 7. The binomial expansion.- XV Series.- 1. Convergent series.- 2. Series with positive terms.- 3. The integral test.- 4. Absolute convergence.- 5. Power series.- 6. Differentiation and integration of power series.- Appendix 1. ? and ?.- 1. Least upper bound.- 2. Limits.- 3. Points of accumulation.- 4. Continuous functions.- Appendix 2. Physics and Mathematics.- Answers.- Supplementary Exercises. Review From the reviews:"...Langs present book is a source of interesting ideas and brilliant techniques."Acta Scientarium Mathematicarum"... It is an admirable straightforward introduction to calculus."Mathematika"A First Course in Calculus went through five editions since the early sixties. Now the original edition of A First Course in Calculus is available again. The approach is the one that was successful decades ago, involving clarity and adjusted to a time when the students background was not as substantial as it might have been. … The audience is intended to consist of those taking the first calculus course, in high school or college." (G. Kirlinger, Internationale Mathematische Nachrichten, Vol. 57 (193), 2003)"This is a reprint of the original edition of Langs A first course in calculus, which was first published in 1964. … The treatment is as rigorous as any mathematician would wish it … . There are quite a lot of exercises … they are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging. … There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." (Gerry Leversha, The Mathematical Gazette, Vol. 86 (507), 2002) Promotional Springer Book Archives Long Description This is a reprint of A First Course in Calculus, which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students Review Text From the reviews: "...Langs present book is a source of interesting ideas and brilliant techniques." Acta Scientarium Mathematicarum "... It is an admirable straightforward introduction to calculus." Mathematika "A First Course in Calculus went through five editions since the early sixties. Now the original edition of A First Course in Calculus is available again. The approach is the one that was successful decades ago, involving clarity and adjusted to a time when the studentsa? background was not as substantial as it might have been. a? The audience is intended to consist of those taking the first calculus course, in high school or college." (G. Kirlinger, Internationale Mathematische Nachrichten, Vol. 57 (193), 2003) "This is a reprint of the original edition of Langas A first course in calculus, which was first published in 1964. a? The treatment is aas rigorous as any mathematician would wish ita? a? . There are quite a lot of exercises a? they are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging. a? There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." (Gerry Leversha, The Mathematical Gazette, Vol. 86 (507), 2002) Review Quote From the reviews:"...Langs present book is a source of interesting ideas and brilliant techniques."Acta Scientarium Mathematicarum"... It is an admirable straightforward introduction to calculus."Mathematika"A First Course in Calculus went through five editions since the early sixties. Now the original edition of A First Course in Calculus is available again. The approach is the one that was successful decades ago, involving clarity and adjusted to a time when the students background was not as substantial as it might have been. … The audience is intended to consist of those taking the first calculus course, in high school or college." (G. Kirlinger, Internationale Mathematische Nachrichten, Vol. 57 (193), 2003)"This is a reprint of the original edition of Langs A first course in calculus, which was first published in 1964. … The treatment is as rigorous as any mathematician would wish it … . There are quite a lot of exercises … they are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging. … There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." (Gerry Leversha, The Mathematical Gazette, Vol. 86 (507), 2002) Feature Covers all of the topics traditionally taught in the first-year claculus sequence in a brief and elementary fashion Description for Sales People This is a reprint of the original edition of Langs classic book "A First Course in Calculus". It covers all of the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. The audience consists of those taking the first calculus course, in high school or college. "..Langs present book is a source of interesting ideas and brilliant techniques." Acta Scientiarum Mathematicarum. "..It is an admirable straightforward introduction to calculus." Mathematika. Details ISBN0387953272 Author Serge Lang Short Title SHORT CALCULUS Series Undergraduate Texts in Mathematics Language English ISBN-10 0387953272 ISBN-13 9780387953274 Media Book Format Paperback DEWEY 515 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States Birth 1927 Residence New Haven, CT, US Death 2005 Pages 260 DOI 10.1007/b84538;10.1007/978-1-4613-0077-9 AU Release Date 2001-11-29 NZ Release Date 2001-11-29 US Release Date 2001-11-29 UK Release Date 2001-11-29 Publisher Springer-Verlag New York Inc. Edition Description Reprint of the 1st ed. Addison-Wesley, 1964. Year 2001 Publication Date 2001-11-29 Subtitle The Original Edition of "A First Course in Calculus" Illustrations XII, 260 p. Audience Undergraduate We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! 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