Short Calculus: The Original Edition of “A First Course in Calculus” (Undergraduate Texts in Mathematics)

Main subject categories: • One-variable Calculus • Real FunctionsMathematics Subjects Classifications (2000): • 26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions • 26A06 One-variable calculusFrom the reviews "This is a reprint of the original edition of Lang’s ‘A First Course in Calculus’, which was first published in 1964....The treatment is ‘as rigorous as any mathematician would wish it’....[The exercises] 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." --Mathematical Gazette 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'background Was Not As Substantial As It Might Be. We Are Now Back To Those Times, So It's 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. Numbers And Functions -- Graphs And Curves -- The Derivative -- Sine And Cosine -- The Mean Value Theorem -- Sketching Curves -- Inverse Functions -- Exponents And Logarithms -- Integration -- Properties Of The Integral -- Techniques Of Integration -- Some Substantial Exercises -- Applications Of Integration -- Taylor's Formula -- Series -- Appendix 1. Epsilon And Delta -- Appendix 2. Physics And Mathematics -- Answers -- Index. By Serge Lang. Praise for the first edition:'..Lang's 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. 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 that 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 it is 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. Front Cover Title Page © Page Foreword Contents CHAPTER I Numbers and Functions CHAPTER II Graphs and Curves CHAPTER III The Derivative CHAPTER IV Sine and Cosine CHAPTER V The Mean Value Theorem CHAPTER VI Sketching Curves CHAPTER VII Inverse Functions CHAPTER VIII Exponents and Logarithms CHAPTER IX Integration CHAPTER X Properties of the Integral CHAPTER XI Techniques of Integration CHAPTER XII Some Substantial Exercises CHAPTER XIII Applications of Integration CHAPTER XIV Taylor's Formula CHAPTER XV Series Appendix 1 epsilon and delta Appendix 2 Physics and Mathematics ANSWERS TO EXERCISES SUPPLEMENTARY EXERCISES INDEX Covers the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. This title is suitable for those taking the first calculus course, in high school or college. In starting the study of any sort of mathematics, we cannot prove everything.