Produktbild: Examples and Theorems in Analysis

Examples and Theorems in Analysis

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

12.12.2003

Abbildungen

X, 287 p.

Verlag

Springer London

Seitenzahl

287

Maße (L/B/H)

23,5/17,8/1,7 cm

Gewicht

526 g

Auflage

Softcover reprint of the original 1st edition 2004

Sprache

Englisch

ISBN

978-1-85233-493-2

Beschreibung

Rezension

From the reviews:


"This book is a unique and very practical contribution to the teaching of calculus … . The aim of this book is to try to give the subject concreteness and immediacy by giving the well-chosen examples equal status with the theorems. … this excellent book is written primarily for first- and second-year undergraduates in mathematics; but it will also be of interest to students of statistics, computer science and engineering … . We warmly recommend it as an entertaining and stimulating companion …"
(Ferenc Móricz, Acta Scientiarum Mathematicarum, 71, 2005)


"This book takes a unique and very practical approach to mathematical analysis. It makes the subject more accessible by giving the examples equal status with the theorems. … A number of applications show what the subject is about, and what can be done with it … . Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems."
(L'enseignement mathématique, 50:1-2, 2004)


"The author presents a book on analysis in which theorems and examples are equally important. … It is a good textbook for students … to obtain a more complete picture of the material and to master basic methods of work in mathematical analysis." (EMS Newsletter, March, 2005)

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

12.12.2003

Abbildungen

X, 287 p.

Verlag

Springer London

Seitenzahl

287

Maße (L/B/H)

23,5/17,8/1,7 cm

Gewicht

526 g

Auflage

Softcover reprint of the original 1st edition 2004

Sprache

Englisch

ISBN

978-1-85233-493-2

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: ProductSafety@springernature.com

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  • Produktbild: Examples and Theorems in Analysis
  • 1. Sequences.- 1.1 Examples, Formulae and Recursion.- 1.2 Monotone and Bounded Sequences.- 1.3 Convergence.- 1.4 Subsequences.- 1.5 Cauchy Sequences.- Exercises.- 2. Functions and Continuity.- 2.1 Examples.- 2.2 Monotone and Bounded Functions.- 2.3 Limits and Continuity.- 2.4 Bounds and Intermediate Values.- 2.5 Inverse Functions.- 2.6 Recursive Limits and Iteration.- 2.7 One-Sided and Infinite Limits. Regulated Functions.- 2.8 Countability.- Exercises.- 3. Differentiation.- 3.1 Differentiable Functions.- 3.2 The Significance of the Derivative.- 3.3 Rules for Differentiation.- 3.4 Mean Value Theorems and Estimation.- 3.5 More on Iteration.- 3.6 Optimisation.- Exercises.- 4. Constructive Integration.- 4.1 Step Functions.- 4.2 The Integral of a Regulated function.- 4.3 Integration and Differentiation.- 4.4 Applications.- 4.5 Further Mean Value Theorems.- Exercises.- 5. Improper Integrals.- 5.1 Improper Integrals on an Interval.- 5.2 Improper Integrals at Infinity.- 5.3 The Gamma function.- Exercises.- 6. Series.- 6.1 Convergence.- 6.2 Series with Positive Terms.- 6.3 Series with Arbitrary Terms.- 6.4 Power Series.- 6.5 Exponential and Trigonometric Functions.- 6.6 Sequences and Series of Functions.- 6.7 Infinite Products.- Exercises.- 7. Applications.- 7.1 Fourier Series.- 7.2 Fourier Integrals.- 7.3 Distributions.- 7.4 Asymptotics.- 7.5 Exercises.- A. Fubini’s Theorem.- B. Hints and Solutions for Exercises.