# Sequences And Series

(6 customer reviews)

175

Authors: Arumugam S, Thangapandi Isaac A, Somasundaram A

ISBN: 9789388005128

Copy Right Year: 2019

Pages:  252

Binding: Soft Cover

Publisher:  Yes Dee Publishing

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## Description

This is a textbook designed to meet the requirements of undergraduate students in Mathematics. It can be comfortably covered in one semester. The content has been tested in the classroom by several professors over the past

Weight .25 kg 22 × 14 × 2 cm

## Table of Content

Chapter 1 PRELIMINARIES
1.1 Introduction
1.2 Sets and Functions
1.3 Intervals in R
1.4 Bounded Sets
1.5 Bounded Functions
Chapter 2 INEQUALITIES
2.1 Introduction
2.2 Inequalities
2.3 Triangle Inequalities
2.4 The Arithmetic, Geometric and Harmonic Means
2.5 Cauchy-Schwarz Inequality
2.6 Some More Inequalities
2.7 Miscellaneous Solved Problems
Chapter 3 SEQUENCES
3.1 Introduction
3.2 Sequences
3.3 Bounded Sequences
3.4 Monotonic Sequences
3.5 Convergent Sequences
3.6 Divergent and Oscillating Sequences
3.7 The Algebra of Limits
3.8 Behaviour of Monotonic Sequences
3.9 Some Theorems on Limits
3.10 Sub sequences
3.11 Limit Points
3.12 Cauchy Sequences
3.13 The Upper and Lower Limits of a Sequence
Chapter 4 SERIES OF POSITIVE TERMS
4.1 In_nite Series
4.2 Comparison Test
4.3 Kummer’s Test
4.4 Root Test and Condensation Test
4.5 Integral Test
Chapter 5 SERIES OF ARBITRARY TERMS
5.1 Alternating Series
5.2 Absolute convergence
5.3 Tests for Convergence of Series of Arbitrary Terms
5.4 Rearrangement (Derangement) of series
5.5 Multiplication of Series
Chapter 6 SEQUENCES AND SERIES OF FUNCTIONS
6.1 Introduction
6.2 Pointwise Convergence
6.3 Uniform Convergence
6.4 Test for Uniform Convergence
6.5 Power Series

• OBJECTIVE TYPE QUESTIONS

Dr. S. Arumugam is currently senior professor (research) and director, National Centre for Advanced research in Mathematics (n-CARDMATH), Kalasalingam Academy of Research and Education, Krishnankoil, India. He has completed 50 years of academic life and has authored 30 books including two textbooks in Tamil. He has organized 27 conferences and workshops and has edited 12 proceedings. He has guided 44 Ph.D candidates and has published around 250 papers in national and international journals. His areas of research interest are graph theory and applications, biological networks, social networks, visual cryptography and topological projective planes. He has served as visiting/adjunct/conjoint professor in several universities in Australia, UK and USA. He has visited more than 20 countries for delivering invited talks in conferences. He is the founder editor-in-chief of AKCE International Journal of Graphs and Combinatorics.

Mr. A. Thangapandi Isaac, who got retired as head of the department of Mathematics, St. John’s College, Palayamkottai has 30 years of experience in teaching. He is also a coauthor of around 20 books along with Professor S. Arumugam.

Dr. A. Somasundaram is presently working as an associate professor at Birla Institute of Technology and Science Pilani – Dubai campus. He is having 22 years of experience in teaching and research in Mathematics. His research areas include fuzzy graphs, domination in graphs and network science. He has to his credit several publications in standard international journals. He is also a coauthor of five textbooks.

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