Author | Clapham, C. R. J. author |
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Title | Introduction to Mathematical Analysis [electronic resource] / by C. R. J. Clapham |
Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 1973 |
Connect to | http://dx.doi.org/10.1007/978-94-011-6572-3 |
Descript | VII, 83 p. 3 illus. online resource |
Content -- 1. Axioms for the Real Numbers -- 1 Introduction -- 2 Fields -- 3 Order -- 4 Completeness -- 5 Upper bound -- 6 The Archimedean property -- Exercises -- 2. Sequences -- 7 Limit of a sequence -- 8 Sequences without limits -- 9 Monotone sequences -- Exercises -- 3. Series -- 10 Infinite series -- 11 Convergence -- 12 Tests -- 13 Absolute convergence -- 14 Power series -- Exercises -- 4. Continuous Functions -- 15 Limit of a function -- 16 Continuity -- 17 The intermediate value property -- 18 Bounds of a continuous function -- Exercises -- 5. Differentiable Functions -- 19 Derivatives -- 20 Rolleโs theorem -- 21 The mean value theorem -- Exercises -- 6. The Riemann Integral -- 22 Introduction -- 23 Upper and lower sums -- 24 Riemann-integrable functions -- 25 Examples -- 26 A necessary and sufficient condition -- 27 Monotone functions -- 28 Uniform continuity -- 29 Integrability of continuous functions -- 30 Properties of the Riemann integral -- 31 The mean value theorem -- 32 Integration and differentiation -- Exercises -- Answers to the Exercises