Intermediate Real Analysis

1. Front Matter

   Pages i-xiv

   PDF

2. Preliminaries

   • Emanuel Fischer

   Pages 1-41

3. Functions

   • Emanuel Fischer

   Pages 42-91

4. Real Sequences and Their Limits

   • Emanuel Fischer

   Pages 92-150

5. Infinite Series of Real Numbers

   • Emanuel Fischer

   Pages 151-201

6. Limit of Functions

   • Emanuel Fischer

   Pages 202-239

7. Continuous Functions

   • Emanuel Fischer

   Pages 240-289

8. Derivatives

   • Emanuel Fischer

   Pages 290-339

9. Convex Functions

   • Emanuel Fischer

   Pages 340-377

10. L’Hôpital’s Rule—Taylor’s Theorem

    • Emanuel Fischer

    Pages 378-426

11. The Complex Numbers. Trigonometric Sums. Infinite Products

    • Emanuel Fischer

    Pages 427-493

12. More on Series: Sequences and Series of Functions

    • Emanuel Fischer

    Pages 494-557

13. Sequences and Series of Functions II

    • Emanuel Fischer

    Pages 558-600

14. The Riemann Integral I

    • Emanuel Fischer

    Pages 601-680

15. The Riemann Integral II

    • Emanuel Fischer

    Pages 681-709

16. Improper Integrals. Elliptic Integrals and Functions

    • Emanuel Fischer

    Pages 710-763

17. Back Matter

    Pages 764-770

    PDF

There are a great deal of books on introductory analysis in print today, many written by mathematicians of the first rank. The publication of another such book therefore warrants a defense. I have taught analysis for many years and have used a variety of texts during this time. These books were of excellent quality mathematically but did not satisfy the needs of the students I was teaching. They were written for mathematicians but not for those who were first aspiring to attain that status. The desire to fill this gap gave rise to the writing of this book. This book is intended to serve as a text for an introductory course in analysis. Its readers will most likely be mathematics, science, or engineering majors undertaking the last quarter of their undergraduate education. The aim of a first course in analysis is to provide the student with a sound foundation for analysis, to familiarize him with the kind of careful thinking used in advanced mathematics, and to provide him with tools for further work in it. The typical student we are dealing with has completed a three-semester calculus course and possibly an introductory course in differential equations. He may even have been exposed to a semester or two of modern algebra. All this time his training has most likely been intuitive with heuristics taking the place of proof. This may have been appropriate for that stage of his development.

• Differentialrechnung
• Fischer
• Integralrechnung
• calculus
• real analysis

• Department of Mathematics, Adelphi University, Garden City, USA

  Emanuel Fischer

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