Introduction to Calculus
Introduction to Calculus (2nd Edition)
2nd Edition
Published on 14. July 2014
332 pages
978-1-4832-2262-2 (ISBN)
Description
The English edition does not differ essentially from the Polish one. Among the more important supplements I should mention § 6.5 containing elementary information on the notation of mathematical logic. To this supplement I was inclined by the experience of many years. For many students (not for all, perhaps) the notation of definitions of certain notions by means of the logical symbols makes it easier to understand these notions (e.g. the notions of uniform continuity or uniform convergence). Besides that, this supplement is included in the book in such a manner that it can be omitted in reading the whole book. Among other changes introduced in the English text, I should mention the addition of a number of exercises and problems; in the second English edition, many of them have been collected in the Supplement. I am glad also to mention the simplification of certain proofs, and finally the removal of mistakes which were found in the primary text
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Content
- Front Cover
- Introduction to Calculus
- Copyright Page
- Table of Contents
- PREFACE TO THE SECOND ENGLISH EDITION
- PREFACE TO THE POLISH EDITION
- CHAPTER I. SEQUENCES AND SERIES
- § 1. INTRODUCTION
- § 2. INFINITE SEQUENCES
- § 3. INFINITE SERIES
- CHAPTER II. FUNCTIONS
- § 4. FUNCTIONS AND THEIR LIMITS
- § 5. CONTINUOUS FUNCTIONS
- § 6. SEQUENCES AND SERIES OF FUNCTIONS
- CHAPTER III. DIFFERENTIAL CALCULUS
- § 7. DERIVATIVES OF THE FIRST ORDER
- § 8. DERIVATIVES OF HIGHER ORDERS
- CHAPTER IV. INTEGRAL CALCULUS
- § 9. INDEFINITE INTEGRALS
- § 10. DEFINITE INTEGRALS
- § 11. IMPROPER INTEGRALS AND THEIR CONNECTION WITH INFINITE SERIES
- SUPPLEMENT: ADDITIONAL EXERCISES
- INDEX
