Sequences of Real and Complex Numbers

Sequences, in a sense, constitute an introduction to the so called "Higher Mathematics". The notion of the limit, which is a core, fundamental concept in the study of many areas of Advanced Mathematics, Physical Sciences and Engineering, is introduced in sequences.
Many important areas in Mathematics, with a wide range of applications, in Physical Sciences and Engineering, like Infinite Series, Derivatives, Integrals, etc, rely heavily on the notion of the limit, and therefore on sequences.
This textbook is written to provide any possible assistance to the students who are first being introduced to the theory of sequences, but it could, equally well, be used by students already exposed to the theory and wishing to broaden their theoretical background and analytical skills on the subject.
The content of this book is divided into 16 chapters, as shown in the table of contents.
Topics covered include fundamental concepts and definitions on limits, bounded and monotone sequences, sub sequences, general theorems on limits including the Cauchy's n-th root theorem and the Cauchy's three means theorem, Cauchy sequences, extensive and detailed treatment of recursive sequences, accumulation points, sequences with complex terms and related theorems, special techniques for evaluating limits, with the aid of differential and integral calculus, the Euler's number e, and other remarkable limits, etc.
The 93 worked out characteristic examples and the 260 problems to be solved, are designed to help students gain confidence and enhance their understanding, working knowledge and computational skills on sequences.
A brief hint or a detailed outline of the procedure to be followed, in solving the more complicated problems, is often given.
Finally, answers to the odd numbered problems, are also given, so that the students can easily verify the validity of their own solution.


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