Problems in mathematical analysis. I. Real numbers, sequences and series - Kaczor, W. J. (Wiesława J.), 1949-; Nowak, M. T. (Maria T.), 1951- (Providence, RI : American Mathematical Society, 2000)
"This book is mainly intended for students studying the basic principles of analysis. However, given its organization, level, and selection of problems, it would also be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. The volume is also suitable for self-study.".
"Each section of the book begins with relatively simple exercises, yet may also contain quite challenging problems. Very often a few consecutive exercises are concerned with different aspects of one mathematical problem or theorem. This presentation of material is designed to help student comprehension and to encourage them to ask their own questions and to start research. The collection of problems in the book is also intended to help teachers who wish to incorporate the problems into lectures.
Solutions for all the problems are provided."--BOOK JACKET.
Ch. 1. Real Numbers. 1.1. Supremum and Infimum of Sets of Real Numbers, Continued Fractions. 1.2. Some Elementary Inequalities -- Ch. 2. Sequences of Real Numbers. 2.1. Monotonic Sequences. 2.2. Limits, Properties of Convergent Sequences. 2.3. The Toeplitz Transformation, the Stolz Theorem and their Applications. 2.4. Limit Points. Limit Superior and Limit Inferior. 2.5. Miscellaneous Problems -- Ch. 3. Series of Real Numbers. 3.1. Summation of Series. 3.2. Series of Nonnegative Terms. 3.3. The Integral Test. 3.4. Series of Positive and Negative Terms - Convergence, Absolute Convergence, Theorem of Leibniz. 3.5. The Dirichlet and Abel Tests. 3.6. Cauchy Product of Infinite Series. 3.7. Rearrangement of Series, Double Series. 3.8. Infinite Products.
Includes bibliographical references.
Keywords: Mathematical analysis