Cargando…
Mathematical analysis : a straightforward approach /
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 con...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1982.
|
| Edición: | Second edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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
- 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
- 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
- 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)]