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This book is a complete and shelf contained presentation of the fundamentals of Sequences of real and complex numbers and is intended primarily for students of Sciences and Engineering. Infinite Sequences are important tool for all Science and Engineering students.
Sequences, in a sense, constitute an introduction to the so called "Higher Mathematics". The notion of the limit, which is a core, fundamental concept to 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.
Basic Concepts and Definitions
Bounded Sequences
Monotone Sequences
Subsequences
Null Sequences
Convergent Sequences
Divergent Sequences
Basic Sequences for Null and Divergent Sequences
Basic Properties for Convergent Sequences
General Theorems on Limits
The number e and other Remarkable Limits
Recursive Sequences
Cauchy Sequences
Accumulation Points, Limit Superior and Limit Inferior
Sequences of Complex Numbers
Special Techniques for Evaluating Limits