[obm-l] Ajuda programa de analise real.

[niski <fabio@xxxxxxxxx>]

Pessoal, esse semestre vou ter uma materia chamada introducao a analise 
real. Segue a ementa:

1. Números reais: introdução axiomática. Intervalos encaixantes. 
Sequências numéricas. Sequências de Cauchy. Limite superior e inferior. 
Sequências monótona limitadas. 2. Continuidade: teoremas do anulamento, 
do máximo e do mínimo, preservação da conexidade. Continuidade por 
sequências. Continuidade uniforme. 3. Derivabilidade: diferencial e 
teorema do valor médio. 4. Integral de Riemann: definição e exemplos 
especiais. Integrabilidade de funções contínuas e teorema fundamental do 
Cálculo. Critérios de Integrabilidade. 5. Séries numéricas e critérios 
de convergência. 6. Sequências e séries de funções: convergência pontual 
e uniforme, teste M de Weierstrass. Continuidade, integrabilidade e 
derivabilidade com convergência uniforme. Séries de potências e 
propriedades.

Tenho um livro aqui intitulado Undergraduate analysis do lang
segue os topicos do livro

Preface
0 Sets and Mappings
0.2 Mappings
0.3 Natural Numbers and Induction
0.4 Denumerable Sets
0.5 Equivalence Relations
I Real Numbers
I.1 Algebraic Axioms
I.2 Ordering Axioms
I.3 Integers and Rational Numbers
I.4 The Completeness Axiom
II Limits and Continuous Functions
II.1 Sequences of Numbers
II.2 Functions and Limits
II.3 Limits with Infinity
II.4 Continuous Functions
III Differentiation
III.1 Properties of the Derivative
III.2 Mean Value Theorem
III.3 Inverse Functions
IV Elementary Functions
IV.1 Exponential
IV.2 Logarithm
IV.3 Sine and Cosine
IV.4 Complex Numbers
V The Elementary Real Integral
V.2 Properties of the Integral
V.3 Taylor's Formula
V.4 Asymptotic Estimates and Stirling's Formula
VI Normed Vector Spaces
VI.2 Normed Vector Spaces
VI.3 n-Space and Function Spaces
VI.4 Completeness
VI.5 Open and Closed Sets
VII Limits
VII.1 Basic Properties
VII.2 Continuous Maps
VII.3 Limits in Function Spaces
VIII Compactness
VIII.1 Basic Properties of Compact Sets
VIII.2 Continuous Maps on Compact Sets
VIII.4 Relation with Open Coverings
IX Series
IX.2 Series of Positive Numbers
IX.3 Non-Absolute Convergence
IX.5 Absolute and Uniform Convergence
IX.6 Power Series
IX.7 Differentiation and Integration of Series
X The Integral in One Variable
X.3 Approximation by Step Maps
X.4 Properties of the Integral
X.6 Relation Between the Integral and the
Derivative
XI Approximation with Convolutions
XI.1 Dirac Sequences
XI.2 The Weierstrass Theorem
XII Fourier Series
XII.1 Hermitian Products and Orthogonality
XII.2 Trigonometric Polynomials as a Total Family
XII.3 Explicit Uniform Approximation
XII.4 Pointwise Convergence
XIII Improper Integrals
XIII.1 Definition
XIII.2 Criteria for Convergence
XIII.3 Interchanging Derivatives and
Integrals
XIV The Fourier Integral
XIV.1 The Schwartz Space
XIV.2 The Fourier Inversion Formula
XIV.3 An Example of Fourier Transform Not
in the Schwartz Space
XV Functions on n-Space
XV.1 Partial Derivatives
XV.2 Differentiability and the Chain Rule
XV.3 Potential Functions
XV.4 Curve Integrals
XV.5 Taylor's Formula
XV.6 Maxima and the Derivative
XVI The Winding Number and Global Potential Functions
XVI.2 The Winding Number and Homology
XVI.5 The Homotopy Form of the
Integrability Theorem
XVI.6 More on Homotopies
XVII Derivatives in Vector Spaces
XVII.1 The Space of Continuous Linear Maps
XVII.2 The Derivative as a Linear Map
XVII.3 Properties of the Derivative
XVII.4 Mean Value Theorem
XVII.5 The Second Derivative
XVII.6 Higher Derivatives and Taylor's Formula
XVIII Inverse Mapping Theorem
XVIII.1 The Shrinking Lemma
XVIII.2 Inverse Mappings, Linear Case
XVIII.3 The Inverse Mapping Theorem
XVIII.5 Product Decompositions
XIX Ordinary Differential Equations
XIX.1 Local Existence and Uniqueness
XIX.3 Linear Differential Equations
XX Multiple Integrals
XX.1 Elementary Multiple Integration
XX.2 Criteria for Admissibility
XX.3 Repeated Integrals
XX.4 Change of Variables
XX.5 Vector Fields on Spheres
XXI Differential Forms
XXI.1 Definitions
XXI.2 Inverse Image of a Form
XXI.4 Stokes' Formula for Simplices

Pergunto, o livro é bom para essa materia que vou ter? tem coisa a mais? 
coisa a menos?

obrigado

-- 
Niski - http://www.linux.ime.usp.br/~niski

"When we ask advice, we are usually looking for an accomplice."
Joseph Louis LaGrange

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