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Titre : Basic Analysis I : Functions of a Real Variable Type de document : document électronique Auteurs : K. Peterson James Editeur : Boca Raton : CRC Press Année de publication : 2020 Importance : 1 vol (580 p.) ISBN/ISSN/EAN : 978-1-351-67944-2 Langues : Français (fre) Catégories : Bibliothèque numérique:Mathématique Mots-clés : Mathematical analysis:Textbooks
Analytic functions:Textbooks
Functions of real variables:TextbooksIndex. décimale : 515.8 Fonctions de variables réelles (analyse réelle) Résumé :
Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth.Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositionsNote de contenu :
TABLE OF CONTENTS
I. Introduction.
II. Understanding Smoothness.
2. Proving Propositions.
3. Sequences of Real Numbers.
4. BolzanoWeierstrass Results.
5. Topological Compactness.
6. Function Limits.
7. Continuity.
8. Consequences of continuity of intervals.
9. Lower Semicontinuous and Convex Functions.
10. Basic Differentiability.
11. The Properties of Derivatives.
12. Consequences of Derivatives.
13. Exponential and Logarithm Functions.
14. Extremal Theory for One Variable.
15. Differentiation in R2 and R3.
16. Multivariable Extremal Theory.
III. Integration and Sequences of Functions.
17. Uniform Continuity.
18. Cauchy Sequences of Real Numbers.
19. Series of Real Numbers.
20. Series in Gerenal.
21. Integration Theiry.
22. Existence of Reimann Integral Theories.
23. The Fundamental Theorem of Calculus (FTOC).
24. Convergence of sequences of functions.
25. Series of Functions and Power Series.
26. Riemann Integration: Discontinuities and Compositions.
27. Fourier Series.
28. Application.
IV. Summing it All Up .
29. Summary.
V. References.
VI. Detailed References.
Côte titre : E-Fs/0059 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Basic Analysis I : Functions of a Real Variable [document électronique] / K. Peterson James . - Boca Raton : CRC Press, 2020 . - 1 vol (580 p.).
ISBN : 978-1-351-67944-2
Langues : Français (fre)
Catégories : Bibliothèque numérique:Mathématique Mots-clés : Mathematical analysis:Textbooks
Analytic functions:Textbooks
Functions of real variables:TextbooksIndex. décimale : 515.8 Fonctions de variables réelles (analyse réelle) Résumé :
Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth.Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositionsNote de contenu :
TABLE OF CONTENTS
I. Introduction.
II. Understanding Smoothness.
2. Proving Propositions.
3. Sequences of Real Numbers.
4. BolzanoWeierstrass Results.
5. Topological Compactness.
6. Function Limits.
7. Continuity.
8. Consequences of continuity of intervals.
9. Lower Semicontinuous and Convex Functions.
10. Basic Differentiability.
11. The Properties of Derivatives.
12. Consequences of Derivatives.
13. Exponential and Logarithm Functions.
14. Extremal Theory for One Variable.
15. Differentiation in R2 and R3.
16. Multivariable Extremal Theory.
III. Integration and Sequences of Functions.
17. Uniform Continuity.
18. Cauchy Sequences of Real Numbers.
19. Series of Real Numbers.
20. Series in Gerenal.
21. Integration Theiry.
22. Existence of Reimann Integral Theories.
23. The Fundamental Theorem of Calculus (FTOC).
24. Convergence of sequences of functions.
25. Series of Functions and Power Series.
26. Riemann Integration: Discontinuities and Compositions.
27. Fourier Series.
28. Application.
IV. Summing it All Up .
29. Summary.
V. References.
VI. Detailed References.
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Titre : Basic Analysis II : A Modern Calculus in Many Variables Type de document : document électronique Auteurs : K. Peterson James Editeur : Boca Raton : CRC Press Année de publication : 2020 Importance : 1 vol (517 p.) ISBN/ISSN/EAN : 978-1-351-67932-9 Langues : Français (fre) Catégories : Bibliothèque numérique:Mathématique Mots-clés : Mathematical analysis:Textbooks
Functions of several real variablesIndex. décimale : 515.8 Fonctions de variables réelles (analyse réelle) Résumé :
Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositionsNote de contenu :
TABLE OF CONTENTS
I- Introduction
1. Beginning Remarks
II- Linear mappings
2.Preliminaries
3.Vector Spaces
4.Linear Transformations
5.Symmetric Matrices
6.Continuity and Topology
7.Abstract Symmetric Matrices
8.Rotations and Orbital Mechanics
9.Determinants and Matrix Manipulations
III- Calculus of Many Variables
10.Differentiability
11.Multivariable Extremal Theory
12.The Inverse and Implicit Function Theorems
13.Linear Approximation Applications
IV- Integration
14.Integration in Multiple Dimensions
15.Change of Variables and Fubini’s Theorem
16.Line Integrals
17.Differential Forms
V Applications
18.The Exponential Matrix
19.Nonlinear Parametric Optimization Theory
VI Summing It All Up
20 Summing It All Up
VII References
IndexCôte titre : E-Fs/0060 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Basic Analysis II : A Modern Calculus in Many Variables [document électronique] / K. Peterson James . - Boca Raton : CRC Press, 2020 . - 1 vol (517 p.).
ISBN : 978-1-351-67932-9
Langues : Français (fre)
Catégories : Bibliothèque numérique:Mathématique Mots-clés : Mathematical analysis:Textbooks
Functions of several real variablesIndex. décimale : 515.8 Fonctions de variables réelles (analyse réelle) Résumé :
Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositionsNote de contenu :
TABLE OF CONTENTS
I- Introduction
1. Beginning Remarks
II- Linear mappings
2.Preliminaries
3.Vector Spaces
4.Linear Transformations
5.Symmetric Matrices
6.Continuity and Topology
7.Abstract Symmetric Matrices
8.Rotations and Orbital Mechanics
9.Determinants and Matrix Manipulations
III- Calculus of Many Variables
10.Differentiability
11.Multivariable Extremal Theory
12.The Inverse and Implicit Function Theorems
13.Linear Approximation Applications
IV- Integration
14.Integration in Multiple Dimensions
15.Change of Variables and Fubini’s Theorem
16.Line Integrals
17.Differential Forms
V Applications
18.The Exponential Matrix
19.Nonlinear Parametric Optimization Theory
VI Summing It All Up
20 Summing It All Up
VII References
IndexCôte titre : E-Fs/0060 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Exemplaires (1)
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Titre : Basic Analysis III : Mappings on Infinite Dimensional Spaces Type de document : document électronique Auteurs : K. Peterson James Editeur : Boca Raton : CRC Press Année de publication : 2020 Importance : 1 vol (458 p.) ISBN/ISSN/EAN : 978-1-351-67929-9 Langues : Français (fre) Catégories : Bibliothèque numérique:Mathématique Mots-clés : Mathematical analysis:Textbooks
Infinite groups
Functional analysisIndex. décimale : 515 -Analysis Résumé :
Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist.Feature: Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositionsNote de contenu :
TABLE OF CONI.
I.Intoduction
1.Intoduction
II. Metric Spaces.
2. Metric Spaces.
3. Completing a Metric Space.
III. Normed Linear Spaces.
4. Vector Spaces.
5. Normed Linear Spaces.
6. Linear Operators on Normed Spaces.
IV. Inner Product Spaces.
7. Inner Product Spaces.
8. Hilbert Spaces.
9. Dual Spaces.
10. Hahn - Banach Results.
11. More About Dual Spaces.
12. Some Classical Results.
V. Operators.
13. Sturm–Liouville Operators.
14. Self Adjoint Operators.
VI. Topics in Applied Modeling.
15. Fields and Charges on a Set.
16. Games.
VII. Summing It All Up.
VIII. References.
IX. Detailed Indices.
Côte titre : E-Fs/0061 En ligne : https://sciences-courses.univ-setif.dz/course/view.php?id=808 Basic Analysis III : Mappings on Infinite Dimensional Spaces [document électronique] / K. Peterson James . - Boca Raton : CRC Press, 2020 . - 1 vol (458 p.).
ISBN : 978-1-351-67929-9
Langues : Français (fre)
Catégories : Bibliothèque numérique:Mathématique Mots-clés : Mathematical analysis:Textbooks
Infinite groups
Functional analysisIndex. décimale : 515 -Analysis Résumé :
Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist.Feature: Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositionsNote de contenu :
TABLE OF CONI.
I.Intoduction
1.Intoduction
II. Metric Spaces.
2. Metric Spaces.
3. Completing a Metric Space.
III. Normed Linear Spaces.
4. Vector Spaces.
5. Normed Linear Spaces.
6. Linear Operators on Normed Spaces.
IV. Inner Product Spaces.
7. Inner Product Spaces.
8. Hilbert Spaces.
9. Dual Spaces.
10. Hahn - Banach Results.
11. More About Dual Spaces.
12. Some Classical Results.
V. Operators.
13. Sturm–Liouville Operators.
14. Self Adjoint Operators.
VI. Topics in Applied Modeling.
15. Fields and Charges on a Set.
16. Games.
VII. Summing It All Up.
VIII. References.
IX. Detailed Indices.
Côte titre : E-Fs/0061 En ligne : https://sciences-courses.univ-setif.dz/course/view.php?id=808 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité E-Fs/0061 E-Fs/0061 E-Book Téléchargeable (PDF) Bibliothéque des sciences Anglais Téléchargeable
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