
02343259
b
2002b.01449
Lang, Serge
Short calculus. The original edition of 'A First Course in Calculus'.
Springer, New York, NY (ISBN 0387953272). 272 p. (2001).
2001
Springer, New York, NY
EN
I15
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 firstyear 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 epsilondeltas, but this does not imply that the book is not rigorous. The book consists of 15 chapters (1. Numbers and Functions, 2. Graphs and Curves, 3. The Derivative, 4. Sine and Cosine, 5. The Mean Value Theorem, 6. Sketching Curves, 7. Inverse Functions, 8. Exponents and Logarithms, 9. Integration, 10. Properties of the Integral, 11. Techniques of Integration, 12. Some Substantial Exercises, 13. Applications of Integration, 14. Taylor's Formula, 15. Series) and two appendices (1. epsilon and delta, 2. Physics and Mathematics). Each chapter 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.