| Description |
1 online resource (xi, 361 pages) : illustrations |
| Contents |
Cover; Title; Copyright; Contents; Preface to the first edition; Preface to the second edition; 1 Real numbers; 1.1 Set notation; 1.2 The set of real numbers; 1.3 Arithmetic; 1.4 Inequalities; 1.9 Roots; 1.10 Quadratic equations; 1.13 Irrational nurnbers; 1.14 Modulus; 2 Continuum property; 2.1 Achilles and the tortoise; 2.2 The continuum property; 2.6 Supremum and infimum; 2.7 Maximum and minimum; 2.9 Intervals; 2.11 Manipulations with sup and inf; 3 Natural numbers; 3.1 Introduction; 3.2 Archimedean property; 3.7 Principle of induction; 4 Convergent sequences; 4.1 The bulldozers and the bee |
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4.2 Sequences4.4 Definition of convergence; 4.7 Criteria for convergence; 4.15 Monotone sequences; 4.21 Some simple properties of convergent sequences; 4.26 Divergent sequences; 5 Subsequences; 5.1 Subsequences; 5.8 Bolzano-Weierstrass theorem; 5.12 Lim sup and lim inf; 5.16 Cauchy sequences; 6 Series; 6.1 Definitions; 6.4 Series of positive terms; 6.7 Elementary properties of series; 6.12 Series and Cauchy sequences; 6.20 Absolute and conditional convergence; 6.23 Manipulations with series; 7 Functions; 7.1 Notation; 7.6 Polynomial and rational functions; 7.9 Combining functions |
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7.11 Inverse functions7.13 Bounded functions; 8 Limits of functions; 8.1 Limits from the left; 8.2 Limits from the right; 8.3 f(x) [rarr] 1as x [rarr] [xi]; 8.6 Continuity at a point; 8.8 Connexion with convergent sequences; 8.11 Properties of limits; 8.16 Limits of composite functions; 8.18 Divergence; 9 Continuity; 9.1 Continuity on an interval; 9.7 Continuity property; 10 Differentiation; 10.1 Derivatives; 10.2 Higher derivatives; 10.4 More notation; 10.5 Properties of differentiable functions; 10.12 Composite functions; 11 Mean value theorems; 11.1 Local maxima and minima |
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11.3 Stationary points11.5 Mean value theorem; 11.9 Taylor's theorem; 12 Monotone functions; 12.1 Definitions; 12.3 Limits of monotone functions; 12.6 Differentiable monotone functions; 12.9 Inverse functions; 12.11 Roots; 12.13 Convex functions; 13 Integration; 13.1 Area; 13.2 The integral; 13.3 Some properties of the integral; 13.9 Differentiation and integration; 13.16 Riemann integral; 13.19 More properties of the integral; 13.27 Improper integrals; 13.31 Euler-Maclaurin summation formula; 14 Exponential and logarithm; 14.1 Logarithm; 14.4 Exponential; 14.6 Powers; 15 Power series |
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15.1 Interval of convergence15.4 Taylor series; 15.7 Continuity and differentiation; 16 Trigonometric functions; 16.1 Introduction; 16.2 Sine and cosine; 16.4 Periodicity; 17 The gamma function; 17.1 Introduction; 17.2 Stirling's formula; 17.4 The gamma function; 17.6 Properties of the gamma function; 18 Vectors; 18.1 Introduction; 18.2 Vectors; 18.4 Length and angle in R[sup(n)]; 18.8 Inequalities; 18.10 Distance; 18.12 Direction; 18.13 Lines; 18.15 Hyperplanes; 18.18 Flats; 18.21 Vector functions; 18.22 Linear and affine functions; 18.26 Convergence of sequences in R[sup(n)] |
| Summary |
For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Mathematical analysis.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Mathematical analysis
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Analyse mathématique.
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| Form |
Electronic book
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| ISBN |
9781139648479 |
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1139648470 |
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9781139171656 |
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1139171658 |
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