Short Calculus: The Original Edition of “A First Course in Calculus”

✍ Scribed by Serge Lang (auth.)

• Publisher: Springer-Verlag New York
• Year: 2002
• Tongue: English
• Leaves: 275
• Series: Undergraduate Texts in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Numbers and Functions....Pages 1-13
Graphs and Curves....Pages 14-34
The Derivative....Pages 35-64
Sine and Cosine....Pages 65-78
The Mean Value Theorem....Pages 79-93
Sketching Curves....Pages 94-106
Inverse Functions....Pages 107-115
Exponents and Logarithms....Pages 116-133
Integration....Pages 134-152
Properties of the Integral....Pages 153-162
Techniques of Integration....Pages 163-177
Some Substantial Exercises....Pages 178-182
Applications of Integration....Pages 183-194
Taylor’s Formula....Pages 195-210
Series....Pages 211-226
Back Matter....Pages 227-263

✦ Subjects

Real Functions