Surprises and counterexamples in real function theory /
Rajwade, A.R.
Surprises and counterexamples in real function theory / by A.R. Rajwade. - Hindustan Book Agency, 2007?
Introduction to the real line ℝ and some of its subsets
A. R. Rajwade, A. K. Bhandari
Pages 1-24
Functions: pathological, peculiar and extraordinary
A. R. Rajwade, A. K. Bhandari
Pages 25-55
The famous everywhere continuous, nowhere differentiable functions: van der Waerden’s and others
A. R. Rajwade, A. K. Bhandari
Pages 56-77
Functions: continuous, periodic, locally recurrent and others
A. R. Rajwade, A. K. Bhandari
Pages 78-110
The Derivative and Higher Derivatives
A. R. Rajwade, A. K. Bhandari
Pages 111-154
Sequences, Harmonic Series, Alternating Series and Related Topics
A. R. Rajwade, A. K. Bhandari
Pages 155-194
The infinite exponential
and Related Topics
A. R. Rajwade, A. K. Bhandari
Pages 195-225
Back Matter
Pages 226-292
This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis.Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II.This book will be useful for students and teachers alike.
8185931712 9788185931715 9789380250168
515.8 / RAJ
Surprises and counterexamples in real function theory / by A.R. Rajwade. - Hindustan Book Agency, 2007?
Introduction to the real line ℝ and some of its subsets
A. R. Rajwade, A. K. Bhandari
Pages 1-24
Functions: pathological, peculiar and extraordinary
A. R. Rajwade, A. K. Bhandari
Pages 25-55
The famous everywhere continuous, nowhere differentiable functions: van der Waerden’s and others
A. R. Rajwade, A. K. Bhandari
Pages 56-77
Functions: continuous, periodic, locally recurrent and others
A. R. Rajwade, A. K. Bhandari
Pages 78-110
The Derivative and Higher Derivatives
A. R. Rajwade, A. K. Bhandari
Pages 111-154
Sequences, Harmonic Series, Alternating Series and Related Topics
A. R. Rajwade, A. K. Bhandari
Pages 155-194
The infinite exponential
and Related Topics
A. R. Rajwade, A. K. Bhandari
Pages 195-225
Back Matter
Pages 226-292
This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis.Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II.This book will be useful for students and teachers alike.
8185931712 9788185931715 9789380250168
515.8 / RAJ