Author | Robdera, Mangatiana A. author |
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Title | A Concise Approach to Mathematical Analysis [electronic resource] / by Mangatiana A. Robdera |
Imprint | London : Springer London : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-0-85729-347-3 |
Descript | XII, 362 p. online resource |
Numbers and Functions -- Real Numbers -- Subsets of ? -- Variables and Functions -- Sequences -- Definition of a Sequence -- Convergence and Limits -- Subsequences -- Upper and Lower Limits -- Cauchy Criterion -- 3. Series -- Infinite Series -- Conditional Convergence -- Comparison Tests -- Root and Ratio Tests -- Further Tests -- 4. Limits and Continuity -- Limits of Functions -- Continuity of Functions -- Properties of Continuous Functions -- Uniform Continuity -- Differentiation -- Derivatives -- Mean Value Theorem -- L'Hรดspital's Rule -- Inverse Function Theorems -- Taylor's Theorem -- Elements of Integration -- Step Functions -- Riemann Integral -- Functions of Bounded Variation -- Riemann-Stieltjes Integral -- Sequences and Series of Functions -- Sequences of Functions -- Series of Functions -- Power Series -- Taylor Series -- Local Structure on the Real Line -- Open and Closed Sets in ? -- Neighborhoods and Interior Points -- Closure Point and Closure -- Completeness and Compactness -- Continuous Functions -- Global Continuity -- Functions Continuous on a Compact Set -- StoneโWeierstrass Theorem -- Fixed-point Theorem -- Ascoli-Arzelร Theorem -- to the Lebesgue Integral -- Null Sets -- Lebesgue Integral -- Improper Integral -- Important Inequalities -- Elements of Fourier Analysis -- Fourier Series -- Convergent Trigonometric Series -- Convergence in 2-mean -- Pointwise Convergence -- A. Appendix -- A.1 Theorems and Proofs -- A.2 Set Notations -- A.3 Cantor's Ternary Set -- A.4 Bernstein's Approximation Theorem -- B. Hints for Selected Exercises