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

ISBN-13: 9780387953274 / Angielski / Miękka / 2001 / 260 str.

Serge Lang; S. Lang

Opis

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 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.

Recenzje

From the reviews:

"...Lang's 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 Lang's 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)

Spis treści

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