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Books, Free Shipping, Analysis

Posted at: Offers to Sell and Export | Posted on: Sun 18 Jul, 2010 8:32 am | Product Category: Reference books [3760]
 
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Books, free shipping, analysis

Product Description:


Contents:

Preface

I - Sets and Functions

§1.

Set Theory

1 - Membership, equality, empty set

2 - The set defined by a relation. Intersections and unions

3 - Whole numbers. Infinite sets

4 - Ordered pairs, Cartesian products, sets of subsets

5 - Functions, maps, correspondences

6 - Injections, surjections, bijections

7 - Equipotent sets. Countable sets

8 - The different types of infinity

9 - Ordinals and cardinals

§2. The logic of logicians

II - Convergence: Discrete variables

§1. Convergent sequences and series

0 - Introduction: what is a real number?

1 - Algebraic operations and the order relation: axioms of R

2 - Inequalities and intervals

3 - Local or asymptotic properties

4 - The concept of limit. Continuity and differentiability

5 - Convergent sequences: definition and examples

6 - The language of series

7 - The marvels of the harmonic series

8 - Algebraic operations on limits

§2. Absolutely convergent series

9 - Increasing sequences. Upper bound of a set of real number

10 - The function log x. Roots of a positive number

11 - What is an integral?

12 - Series with positive terms

13 - Alternating series

14 - Classical absolutely convergent series

15 - Unconditional convergence: general case

16 - Comparison relations. Criteria of Cauchy and d'Alembert

17 - Infinite limits

18 - Unconditional convergence: associativity

§3. First concepts of analytic functions

19 - The Taylor series

20 - The principle of analytic continuation

21 - The function cot x and the series ∑ 1/n2k

22 - Multiplication of series. Composition of analytic functions. Formal series

23 - The elliptic functions of Weierstrass

III- Convergence: Continuous variables

§1. The intermediate value theorem

1 - Limit values of a function. Open and closed sets

2 - Continuous functions

3 - Right and left limits of a monotone function

4 - The intermediate value theorem

§2. Uniform convergence

5 - Limits of continuous functions

6 - A slip up of Cauchy's

7 - The uniform metric

8 - Series of continuous functions. Normal convergence

§3. Bolzano-Weierstrass and Cauchy's criterion

9 - Nested intervals, Bolzano-Weierstrass, compact sets

10 - Cauchy's general convergence criterion

11 - Cauchy's criterion for series: examples

12 - Limits of limits

13 - Passing to the limit in a series of functions

§4. Differentiable functions

14 - Derivatives of a function

15 - Rules for calculating derivatives

16 - The mean value theorem

17 - Sequences and series of differentiable functions

18 - Extensions to unconditional convergence

§5. Differentiable functions of several variables

19 - Partial derivatives and differentials

20 - Differentiability of functions of class C1

21 - Differentiation of composite functions

22 - Limits of differentiable functions

23 - Interchanging the order of differentiation

24 - Implicit functions

Appendix to Chapter III

1 - Cartesian spaces and general metric spaces

2 - Open and closed sets

3 - Limits and Cauchy's criterion in a metric space; complete spaces

4 - Continuous functions

5 - Absolutely convergent series in a Banach space

6 - Continuous linear maps

7 - Compact spaces

8 - Topological spaces

IV - Powers, Exponentials, Logarithms, Trigonometric Functions

§1. Direct construction

1 - Rational exponents

2 - Definition of real powers

3 - The calculus of real exponents

4 - Logarithms to base a. Power functions

5 - Asymptotic behaviour

6 - Characterisations of the exponential, power and logarithmic functions

7 - Derivatives of the exponential functions: direct method

8 - Derivatives of exponential functions, powers and logarithms

§2. Series expansions

9 - The number e. Napierian logarithms

10 - Exponential and logarithmic series: direct method

11 - Newton's binomial series

12 - The power series for the logarithm

13 - The exponential function as a limit

14 - Imaginary exponentials and trigonometric functions

15 - Euler's relation chez Euler

16 - Hyperbolic functions

§3. Infinite products

17 - Absolutely convergent infinite products

18 - The infinite product for the sine function

19 - Expansion of an infinite product in series

20 - Strange identities

§4. The topology of the functions Arg(z) and Log z

Index

Product Details

Author Godement R.

Publisher Higher Education Press

Isbn 9787040279559

Published December 2009

Pages 430

Size 16K

Edition First

Format Paperback

Language Chinese

Page material gelatine plate paper



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