top

  Info

  • Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.

  Info

  • Utilizzare questo link per rimuovere la selezione effettuata.

Biblioteca

MARC Lista (tabellare)
Elementary Real and Complex Analysis
Elementary Real and Complex Analysis
Autore Shilov Georgi E
Edizione [1st ed.]
Pubbl/distr/stampa Newburyport, : Dover Publications, 2012
Descrizione fisica 1 online resource (943 p.)
Disciplina 515
Collana Dover Books on Mathematics
Soggetto topico Mathematical analysis
Engineering & Applied Sciences
Applied Mathematics
ISBN 0-486-13500-4
1-62198-656-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover; Title Page; Copyright Page; Contents; Preface; 1 Real Numbers; 1.1. Set-Theoretic Preliminaries; 1.2. Axioms for the Real Number System; 1.3. Consequences of the Addition Axioms; 1.4. Consequences of the Multiplication Axioms; 1.5. Consequences of the Order Axioms; 1.6. Consequences of the Least Upper Bound Axiom; 1.7. The Principle of Archimedes and Its Consequences; 1.8. The Principle of Nested Intervals; 1.9. The Extended Real Number System; Problems; 2 Sets; 2.1. Operations on Sets; 2.2. Equivalence of Sets; 2.3. Countable Sets; 2.4. Uncountable Sets; 2.5. Mathematical Structures
2.6. n-Dimensional Space2.7. Complex Numbers; 2.8. Functions and Graphs; Problems; 3 Metric Spaces; 3.1. Definitions and Examples; 3.2. Open Sets; 3.3. Convergent Sequences and Homeomorphisms; 3.4. Limit Points; 3.5. Closed Sets; 3.6. Dense Sets and Closures; 3.7. Complete Metric Spaces; 3.8. Completion of a Metric Space; 3.9. Compactness; Problems; 4 Limits; 4.1. Basic Concepts; 4.2. Some General Theorems; 4.3. Limits of Numerical Functions; 4.4. Upper and Lower Limits; 4.5. Nondecreasing and Nonincreasing Functions; 4.6. Limits of Numerical Sequences; 4.7. Limits of Vector Functions
Problems5 Continuous Functions; 5.1. Continuous Functions on a Metric Space; 5.2. Continuous Numerical Functions on the Real Line; 5.3. Monotonie Functions; 5.4. The Logarithm; 5.5. The Exponential; 5.6. Trigonometric Functions; 5.7. Applications of Trigonometric Functions; 5.8. Continuous Vector Functions of a Vector Variable; 5.9. Sequences of Functions; Problems; 6 Series; 6.1. Numerical Series; 6.2. Absolute and Conditional Convergence; 6.3. Operations on Series; 6.4. Series of Vectors; 6.5. Series of Functions; 6.6. Power Series; Problems; 7 The Derivative; 7.1. Definitions and Examples
7.2. Properties of Differentiable Functions7.3. The Differential; 7.4. Mean Value Theorems; 7.5. Concavity and Inflection Points; 7.6. L'Hospital's Rules; Problems; 8 Higher Derivatives; 8.1. Definitions and Examples; 8.2. Taylor's Formula; 8.3. More on Concavity and Inflection Points; 8.4. Another Version of Taylor's Formula; 8.5. Taylor Series; 8.6. Complex Exponentials and Trigonometric Functions; 8.7. Hyperbolic Functions; Problems; 9 The Integral; 9.1. Definitions and Basic Properties; 9.2. Area and Arc Length; 9.3. Antiderivatives and Indefinite Integrals
9.4. Technique of Indefinite Integration9.5. Evaluation of Definite Integrals; 9.6. More on Area; 9.7. More on Arc Length; 9.8. Area of a Surface of Revolution; 9.9. Further Applications of Integration; 9.10. Integration of Sequences of Functions; 9.11. Parameter-Dependent Integrals; 9.12. Line Integrals; Problems; 10 Analytic Functions; 10.1. Basic Concepts; 10.2. Line Integrals of Complex Functions; 10.3. Cauchy's Theorem and Its Consequences; 10.4. Residues and Isolated Singular Points; 10.5. Mappings and Elementary Functions; Problems; 11 Improper Integrals
11.1. Improper Integrals of the First Kind
Record Nr. UNINA-9911006808303321
Shilov Georgi E  
Newburyport, : Dover Publications, 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear Algebra
Linear Algebra
Autore Shilov Georgi E
Edizione [1st ed.]
Pubbl/distr/stampa Newburyport, : Dover Publications, 2012
Descrizione fisica 1 online resource (670 p.)
Disciplina 512/.5
Collana Dover Books on Mathematics
Soggetto topico Algebras, Linear
Mathematics
Physical Sciences & Mathematics
Algebra
ISBN 0-486-13504-7
1-62198-583-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto DOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; PREFACE; Table of Contents; chapter I - DETERMINANTS; I.I. Number Fields; I.2. Problems of the Theory of Systems of Linear Equations; I.3.Determinants of Order n; 1.4. Properties of Determinants; 1.5. Cofactors and Minors; 1.6. Practical Evaluation of Determinants; 1.7. Cramer's Rule; 1.8. Minors of Arbitrary Order. Laplace's Theorem; 1.9. Linear Dependence between Columns; chapter 2 - LINEAR SPACES; 2.1. Definitions; 2.2. Linear Dependence; 2.3 Bases, Components, Dimension; 2.4. Subspaces; 2.5. Linear Manifolds; 2.6. Hyperplanes
2.7. Morphisms of Linear Spaceschapter 3 - SYSTEMS OF LINEAR EQUATIONS; 3.1. More on the Rank of a Matrix; 3.2. Nontrivial Compatibility of a Homogeneous Linear System; 3.3. The Compatibility Condition for a General Linear System; 3.4. The General Solution of a Linear System; 3.5. Geometric Properties of the Solution Space; 3.6. Methods for Calculating the Rank of a Matrix; chapter 4 - LINEAR FUNCTIONS OF A VECTOR ARGUMENT; 4.1. Linear Forms; 4.2. Linear Operators; 4.3. Sums and Products of Operators; 4.4. Corresponding Operations on Matrices; 4.5. Further Properties of Matrix Multiplication
4.6.The Range and Null Space of a Linear Operator4.7. Linear Operators Mapping a Space Kn into Itself 2&; 4.8.Invariant Subspaces; 4.9.Eigenvectors and Eigenvalues; chapter 5 - COORDINATE TRANSFORMATIONS; 5.1. Transformation to a New Basis; 5.2. Consecutive Transformations; 5.3. Transformation of the Components of a Vector; 5.4. Transformation of the Coefficients of a Linear Form; 5.5. Transformation of the Matrix of a Linear Operator; *5.6. Tensors; chapter 6 - THE CANONICAL FORM OF THE MATRIX OF A LINEAR OPERATOR; 6.1 Canonical Form of the Matrix of a Nilpotent Operator .
6.2. Algebras. The Algebra of Polynomials6.3. Canonical Form of the Matrix of an Arbitrary Operator; 6.4. Elementary Divisors; 6.5. Further Implications; 6.6. The Real Jordan Canonical Form; *6.7. Spectra, Jets and Polynomials; *6.8. Operator Functions and Their Matrices; chapter 7 - BILINEAR AND QUADRATIC FORMS; 7.1. Bilinear Forms; 7.2. Quadratic Forms; 7.3. Reduction of a Quadratic Form to Canonical Form; 7.4. The Canonical Basis of a Bilinear Form; 7.5. Construction of a Canonical Basis by Jacobi's Method; 7.6. Adjoint Linear Operators
7.7. Isomorphism of Spaces Equipped with a Bilinear Form*7.8. Multilinear Forms; 7.9. Bilinear and Quadratic Forms in a Real Space; chapter 8 - EUCLIDEAN SPACES; 8.1. Introduction; 8.2. Definition of a Euclidean Space; 8.3. Basic Metric Concepts; 8.4. Orthogonal Bases; 8.5. Perpendiculars; 8.6. The Orthogonalization Theorem; 8.7. The Gram Determinant; 8.8. Incompatible Systems and the Method of Least Squares; 8.9. Adjoint Operators and Isometry; chapter 9 - UNITARY SPACES; 9.1. Hermitian Forms; 9.2. The Scalar Product in a Complex Space; 9.3. Normal Operators
9.4. Applications to Operator Theory in Euclidean Space
Record Nr. UNINA-9911006800003321
Shilov Georgi E  
Newburyport, : Dover Publications, 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui