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BL
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| Record Number
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647145
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| Doc. No
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dltt
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| Main Entry
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Speight, J. M., (J. Martin)
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| Title & Author
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A sequential introduction to real analysis /\ J.M. Speight
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| Series Statement
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Essential textbooks in mathematics,; vol. 1
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| Page. NO
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xxii, 251 pages :: illustrations ;; 24 cm
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| ISBN
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9781783267828 (hardcover : alk. paper)
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: 1783267828 (hardcover : alk. paper)
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: 9781783267835 (pbk. : alk. paper)
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: 1783267836 (pbk. : alk. paper)
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| Bibliographies/Indexes
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Includes bibliographical references (pages 225-226) and index
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| Contents
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Machine generated contents note: ch. 1 Basic properties of the set of real numbers -- 1.1.Recap of set notation -- 1.2.Functions -- 1.3.Boundedness and the Axiom of Completeness -- 1.4.Some consequences of the Axiom of Completeness -- 1.5.Summary -- 1.6.Tutorial problems -- 1.7.Homework problems -- ch. 2 Real sequences -- 2.1.Definition and examples of real sequences -- 2.2.Convergence of a real sequence -- 2.3.Summary -- 2.4.Tutorial problems -- 2.5.Homework problems -- ch. 3 Limit theorems -- 3.1.Some basic limit theorems -- 3.2.The Monotone Convergence Theorem -- 3.3.Sequences and suprema -- 3.4.Summary -- 3.5.Tutorial problems -- 3.6.Homework problems -- ch. 4 Subsequences -- 4.1.Definition and convergence properties -- 4.2.The Bolzano Weierstrass Theorem -- 4.3.Summary -- 4.4.Tutorial problems -- 4.5.Homework problems -- ch. 5 Series -- 5.1.Definition and convergence -- 5.2.Convergence tests for series -- 5.3.Alternating series -- 5.4.Absolute convergence -- 5.5.Summary --
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Note continued: 5.6.Tutorial problems -- 5.7.Homework problems -- ch. 6 Continuous functions -- 6.1.Sequential continuity -- 6.2.Basic properties of continuous functions -- 6.3.The Intermediate Value Theorem -- 6.4.The Extreme Value Theorem -- 6.5.Summary -- 6.6.Tutorial problems -- 6.7.Homework problems -- ch. 7 Some symbolic logic -- 7.1.Statements and their symbolic manipulation -- 7.2.Implications -- 7.3.Quantifiers -- 7.4.Summary -- 7.5.Tutorial problems -- 7.6.Homework problems -- ch. 8 Limits of functions -- 8.1.The main definition -- 8.2.Limits at infinity -- 8.3.Summary -- 8.4.Tutorial problems -- 8.5.Homework problems -- ch. 9 Differentiable functions -- 9.1.The main definition -- 9.2.The rules of differentiation -- 9.3.Functions differentiable on an interval -- 9.4.Higher derivatives and Taylor's Theorem -- 9.5.Summary -- 9.6.Tutorial problems -- 9.7.Homework problems -- ch. 10 Power series -- 10.1.Definition and radius of convergence --
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Note continued: 10.2.Differentiability of power series -- 10.3.Properties of the exponential function -- 10.4.Elementary properties of the trigonometric functions -- 10.5.Summary -- 10.6.Tutorial problems -- 10.7.Homework problems -- ch. 11 Integration -- 11.1.Dissections and Riemann sums -- 11.2.Definition of the Riemann integral -- 11.3.A sequential characterization of integrability -- 11.4.Elementary properties of the Riemann integral -- 11.5.The Fundamental Theorem of the Calculus -- 11.6.Summary -- 11.7.Tutorial problems -- 11.8.Homework problems -- ch. 12 Logarithms and irrational powers -- 12.1.Logarithms -- 12.2.Irrational (and rational) powers -- 12.3.Summary -- 12.4.Tutorial problems -- 12.5.Homework problems -- ch. 13 What are the reals? -- 13.1.What arc the rationals? -- 13.2.The Cauchy property -- 13.3.A sequential construction of the reals
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| Subject
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Mathematical analysis
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| Subject
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Precalculus
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