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 Moricz, 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 mathematique, 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)

• 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.

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 Moricz, 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 mathematique, 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)

• 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.