Author | Howie, John M. author |
---|---|
Title | Real Analysis [electronic resource] / by John M. Howie |
Imprint | London : Springer London : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0341-7 |
Descript | X, 276 p. 13 illus. online resource |
1. Introductory Ideas -- 1.1 Foreword for the Student: Is Analysis Necessary? -- 1.2 The Concept of Number -- 1.3 The Language of Set Theory -- 1.4 Real Numbers -- 1.5 Induction -- 1.6 Inequalities -- 2. Sequences and Series -- 2.1 Sequences -- 2.2 Sums, Products and Quotients -- 2.3 Monotonie Sequences -- 2.4 Cauchy Sequences -- 2.5 Series -- 2.6 The Comparison Test -- 2.7 Series of Positive and Negative Terms -- 3. Functions and Continuity -- 3.1 Functions, Graphs -- 3.2 Sums, Products, Compositions; Polynomial and Rational Functions -- 3.3 Circular Functions -- 3.4 Limits -- 3.5 Continuity -- 3.6 Uniform Continuity -- 3.7 Inverse Functions -- 4. Differentiation -- 4.1 The Derivative -- 4.2 The Mean Value Theorems -- 4.3 Inverse Functions -- 4.4 Higher Derivatives -- 4.5 Taylorโs Theorem -- 5. Integration -- 5.1 The Riemann Integral -- 5.2 Classes of Integrable Functions -- 5.3 Properties of Integrals -- 5.4 The Fundamental Theorem -- 5.5 Techniques of Integration -- 5.6 Improper Integrals of the First Kind -- 5.7 Improper Integrals of the Second Kind -- 6. The Logarithmic and Exponential Functions -- 6.1 A Function Defined by an Integral -- 6.2 The Inverse Function -- 6.3 Further Properties of the Exponential and Logarithmic Functions -- Sequences and Series of Functions -- 7.1 Uniform Convergence -- 7.2 Uniform Convergence of Series -- 7.3 Power Series -- 8. The Circular Functions -- 8.1 Definitions and Elementary Properties -- 8.2 Length -- 9. Miscellaneous Examples -- 9.1 Wallisโs Formula -- 9.2 Stirlingโs Formula -- 9.3 A Continuous, Nowhere Differentiable Function -- Solutions to Exercises -- The Greek Alphabet