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.
Essential ordinary differential equations / / Robert Magnus
| Essential ordinary differential equations / / Robert Magnus |
| Autore | Magnus Robert |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
| Descrizione fisica | 1 online resource (290 pages) |
| Disciplina | 381 |
| Collana | Springer Undergraduate Mathematics |
| Soggetto topico |
Differential equations
Equacions diferencials |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031115318
9783031115301 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Linear Ordinary Differential Equations -- 1.1 First Order Linear Equations -- 1.2 The nth Order Linear Equation -- 1.2.1 The Wronskian -- 1.2.2 Non-homogeneous Equations -- 1.2.3 Complex Solutions -- 1.2.4 Exercises -- 1.2.5 Projects -- 1.3 Homogeneous Linear Equations with Constant Coefficients -- 1.3.1 What to do About Multiple Roots -- 1.3.2 Euler's Equation -- 1.3.3 Exercises -- 1.4 Non-homogeneous Equations with Constant Coefficients -- 1.4.1 How to Calculate a Particular Solution -- 1.4.2 Exercises -- 1.4.3 Projects -- 1.5 Boundary Value Problems -- 1.5.1 Boundary Conditions -- 1.5.2 Green's Function -- Practicalities -- 1.5.3 Exercises -- 2 Separation of Variables -- 2.1 Separable Equations -- 2.1.1 The Autonomous Case -- 2.1.2 The Non-autonomous Case -- 2.1.3 Exercises -- 2.2 One-Parameter Groups of Symmetries -- 2.2.1 Exercises -- 2.3 Newton's Equation -- 2.3.1 Motion in a Regular Level Set -- 2.3.2 Critical Points -- Small Oscillations -- 2.3.3 Exercises -- 2.4 Motion in a Central Force Field -- 3 Series Solutions of Linear Equations -- 3.1 Solutions at an Ordinary Point -- 3.1.1 Preliminaries on Power Series -- 3.1.2 Solution in Power Series at an Ordinary Point -- 3.1.3 Exercises -- 3.1.4 Projects -- 3.2 Solutions at a Regular Singular Point -- 3.2.1 The Method of Frobenius -- 3.2.2 The Second Solution When γ1-γ2 Is an Integer -- Summary of the Second Solution -- 3.2.3 The Point at Infinity -- 3.2.4 Exercises -- 3.2.5 Projects -- 4 Existence Theory -- 4.1 Existence and Uniqueness of Solutions -- 4.1.1 Picard's Theorem and Successive Approximations -- 4.1.2 The nth Order Linear Equation Revisited -- 4.1.3 The First Order Vector Equation -- 4.1.4 Exercises -- 4.1.5 Projects -- 5 The Exponential of a Matrix -- 5.1 Defining the Exponential -- 5.1.1 Exercises -- 5.2 Calculation of Matrix Exponentials.
5.2.1 Eigenvector Method -- 5.2.2 Cayley-Hamilton -- 5.2.3 Interpolation Polynomials -- 5.2.4 Newton's Divided Differences -- 5.2.5 Analytic Functions of a Matrix -- 5.2.6 Exercises -- 5.2.7 Projects -- 5.3 Linear Systems with Variable Coefficients -- 5.3.1 Exercises -- 5.3.2 Projects -- 6 Continuation of Solutions -- 6.1 The Maximal Solution -- 6.1.1 Exercises -- 6.2 Dependence on Initial Conditions -- 6.2.1 Differentiability of ϕx0x -- 6.2.2 Higher Derivatives of ϕx0x -- 6.2.3 Equations with Parameters -- 6.2.4 Exercises -- 6.3 Essential Stability Theory -- 6.3.1 Stability of Equilibrium Points -- 6.3.2 Lyapunov Functions -- 6.3.3 Construction of a Lyapunov Function for the Equation dx/dt=Ax -- 6.3.4 Exercises -- 6.3.5 Projects -- 7 Sturm-Liouville Theory -- 7.1 Symmetry and Self-adjointness -- 7.1.1 Rayleigh Quotient -- 7.1.2 Exercises -- 7.2 Eigenvalues and Eigenfunctions -- 7.2.1 Eigenfunction Expansions -- 7.2.2 Mean Square Convergence of Eigenfunction Expansions -- 7.2.3 Eigenvalue Problems with Weights -- 7.2.4 Exercises -- 7.2.5 Projects -- Afterword -- Index. |
| Record Nr. | UNINA-9910632483703321 |
Magnus Robert
|
||
| Cham, Switzerland : , : Springer, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fundamental Mathematical Analysis [[electronic resource] /] / by Robert Magnus
| Fundamental Mathematical Analysis [[electronic resource] /] / by Robert Magnus |
| Autore | Magnus Robert |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (XX, 433 p. 35 illus., 11 illus. in color.) |
| Disciplina | 515 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Functions of real variables
Sequences (Mathematics) Mathematical analysis Analysis (Mathematics) Real Functions Sequences, Series, Summability Analysis |
| ISBN | 3-030-46321-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 2 Real Numbers -- 3 Sequences and Series -- 4 Functions and Continuity -- 5 Derivatives and Differentiation -- 6 Integrals and Integration -- 7 The Elementary Transcendental Functions -- 8 The Techniques of Integration -- 9 Complex Numbers -- 10 Complex Sequences and Series -- 11 Function Sequences and Function Series -- 12 Improper Integrals -- Index. |
| Record Nr. | UNISA-996418272703316 |
|
Magnus Robert
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Fundamental Mathematical Analysis / / by Robert Magnus
| Fundamental Mathematical Analysis / / by Robert Magnus |
| Autore | Magnus Robert |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (XX, 433 p. 35 illus., 11 illus. in color.) |
| Disciplina | 515 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Functions of real variables
Sequences (Mathematics) Mathematical analysis Analysis (Mathematics) Real Functions Sequences, Series, Summability Analysis |
| ISBN |
9783030463212
3030463214 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 2 Real Numbers -- 3 Sequences and Series -- 4 Functions and Continuity -- 5 Derivatives and Differentiation -- 6 Integrals and Integration -- 7 The Elementary Transcendental Functions -- 8 The Techniques of Integration -- 9 Complex Numbers -- 10 Complex Sequences and Series -- 11 Function Sequences and Function Series -- 12 Improper Integrals -- Index. |
| Record Nr. | UNINA-9910484169703321 |
|
Magnus Robert
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Metric spaces : a companion to analysis / / Robert Magnus
| Metric spaces : a companion to analysis / / Robert Magnus |
| Autore | Magnus Robert |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] |
| Descrizione fisica | 1 online resource (258 pages) |
| Disciplina | 514.32 |
| Collana | Springer undergraduate mathematics series |
| Soggetto topico |
Metric spaces
Mathematics Espais mètrics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030949464
9783030949457 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Preliminaries on Sets -- Basic Relations -- Basic Operations -- Writing Predicates -- Set-Building Rules -- Relations and Functions -- Cardinals -- Other Notions -- 1 Metric Spaces -- 1.1 Metrics -- 1.1.1 Rationale for Metrics -- 1.1.2 Defining Metric Space -- 1.1.3 Exercises -- 1.2 Examples of Metric Spaces -- 1.2.1 Normed Spaces -- 1.2.2 Subspaces -- 1.2.3 Examples -- Not Subspaces of Normed Spaces -- 1.2.4 Pseudometrics -- 1.2.5 Cauchy-Schwarz, Hölder, Minkowski -- 1.2.6 Exercises -- 1.3 Cantor's Middle Thirds Set -- 1.3.1 Exercises -- 1.4 The Normed Spaces of Functional Analysis -- 1.4.1 Sequence Spaces -- 1.4.2 Function Spaces -- 1.4.3 Spaces of Continuous Functions -- 1.4.4 Spaces of Integrable Functions -- 1.4.5 Hölder's and Minkowski's Inequalities for Integrals -- 1.4.6 Exercises -- 2 Basic Theory of Metric Spaces -- 2.1 Balls in a Metric Space -- 2.1.1 Limit of a Convergent Sequence -- 2.1.2 Uniqueness of the Limit -- 2.1.3 Neighbourhoods -- 2.1.4 Bounded Sets -- 2.1.5 Completeness -- a Key Concept -- 2.1.6 Exercises -- 2.2 Open Sets, and Closed -- 2.2.1 Open Sets -- 2.2.2 Union and Intersection of Open Sets -- 2.2.3 Closed Sets -- 2.2.4 Union and Intersection of Closed Sets -- 2.2.5 Characterisation of Open and Closed Sets by Sequences -- 2.2.6 Interior, Closure and Boundary -- 2.2.7 Limit Points of Sets -- 2.2.8 Characterisation of Closure by Limit Points -- 2.2.9 Subspaces -- 2.2.10 Open and Closed Sets in a Subspace -- 2.2.11 Exercises -- 2.3 Continuous Mappings -- 2.3.1 Defining Continuity -- 2.3.2 New Views of Continuity -- 2.3.3 Limits of Functions -- 2.3.4 Characterising Continuity by Sequences -- 2.3.5 Lipschitz Mappings -- 2.3.6 Examples of Continuous Functions -- 2.3.7 Exercises -- 2.4 Continuity of Linear Mappings -- 2.4.1 Continuity Criterion -- 2.4.2 Operator Norms -- 2.4.3 Exercises.
2.5 Homeomorphisms and Topological Properties -- 2.5.1 Equivalent Metrics -- 2.5.2 Exercises -- 2.6 Topologies and σ-Algebras -- 2.6.1 Order Topologies -- 2.6.2 Exercises -- 2.6.3 Pointers to Further Study -- 2.7 () Mazur-Ulam -- 2.7.1 Exercises -- 3 Completeness of the Classical Spaces -- 3.1 Coordinate Spaces and Normed Sequence Spaces -- 3.1.1 Completeness of Rn -- 3.1.2 Completeness of p -- 3.1.3 Exercises -- 3.2 Product Spaces -- 3.2.1 Finitely Many Factors -- 3.2.2 Infinitely Many Factors -- 3.2.3 The Space 2N+ and the Cantor Set -- 3.2.4 Subspaces of Complete Spaces -- 3.2.5 Exercises -- 3.3 Spaces of Continuous Functions -- 3.3.1 Uniform Convergence -- 3.3.2 Series in Normed Spaces -- 3.3.3 The Weierstrass M-Test -- 3.3.4 The Spaces C(R) and Cp(R) -- 3.3.5 Exercises -- 3.4 () Rearrangements -- 3.4.1 Vector Series -- 3.4.2 Exercises -- 3.4.3 Pointers to Further Study -- 3.5 () Invertible Operators -- 3.5.1 Fredholm Integral Equation -- 3.5.2 Exercises -- 3.5.3 Pointers to Further Study -- 3.6 () Tietze -- 3.6.1 Formulas for an Extension -- 3.6.2 Exercises -- 3.6.3 Pointers to Further Study -- 4 Compact Spaces -- 4.1 Sequentially Compact Spaces -- 4.1.1 Continuous Functions on Sequentially Compact Spaces -- 4.1.2 Bolzano-Weierstrass in Rn -- 4.1.3 Sequentially Compact Sets in Rn -- 4.1.4 Sequentially Compact Sets in Other Spaces -- 4.1.5 The Space C(M) -- 4.1.6 Exercises -- 4.2 The Correct Definition of Compactness -- 4.2.1 Thoughts About the Definition -- 4.2.2 Compact Spaces and Compact Sets -- 4.2.3 Continuous Functions on Compact Spaces -- 4.2.4 Uniform Continuity -- 4.2.5 Exercises -- 4.3 Equivalence of Compactness and Sequential Compactness -- 4.3.1 Relative Compactness -- 4.3.2 Local Compactness -- 4.3.3 Exercises -- 4.4 Finite Dimensional Normed Vector Spaces -- 4.4.1 Exercises -- 4.5 () Ascoli -- 4.5.1 Peano's Existence Theorem. 4.5.2 Exercises -- 4.5.3 Pointers to Further Study -- 5 Separable Spaces -- 5.1 Dense Subsets of a Metric Space -- 5.1.1 Defining a Vector-Valued Integral -- 5.1.2 Exercises -- 5.2 Separability -- 5.2.1 Second Countability -- 5.2.2 Exercises -- 5.3 () Weierstrass -- 5.3.1 Exercises -- 5.3.2 Pointers to Further Study -- 5.4 () Stone-Weierstrass -- 5.4.1 Exercises -- 5.4.2 Pointers to Further Study -- 6 Properties of Complete Spaces -- 6.1 Cantor's Nested Intersection Theorem -- Notes About Cantor's Theorem -- 6.1.1 Categories -- Thoughts About the Proof -- 6.1.2 Exercises -- 6.2 () Genericity -- 6.2.1 Exercises -- 6.2.2 Pointers to Further Study -- 6.3 () Nowhere Differentiability -- 6.3.1 Exercises -- 6.3.2 Pointers to Further Study -- 6.4 Fixed Points -- 6.4.1 Exercises -- 6.5 () Picard -- 6.5.1 Exercises -- 6.6 () Zeros -- 6.6.1 Exercises -- 6.6.2 Pointers to Further Study -- 6.7 Completion of a Metric Space -- 6.7.1 Other Ways to Complete a Metric Space -- 6.7.2 Exercises -- 7 Connected Spaces -- 7.1 Connectedness -- 7.1.1 Connected Sets -- 7.1.2 Rules for Connected Sets -- 7.1.3 Connected Subsets of R -- 7.1.4 Exercises -- 7.2 Continuous Mappings and Connectedness -- 7.2.1 Continuous Curves -- 7.2.2 Arcwise Connectedness -- 7.2.3 Exiting a Set -- 7.2.4 Exercises -- 7.3 Connected Components -- 7.3.1 Examples of Connected Components -- 7.3.2 Arcwise Connected Components -- 7.3.3 Exercises -- 7.4 () Peano -- 7.4.1 Exercises -- 7.4.2 Pointers to Further Study -- Afterword -- Index. |
| Record Nr. | UNISA-996466417703316 |
|
Magnus Robert
|
||
| Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Metric spaces : a companion to analysis / / Robert Magnus
| Metric spaces : a companion to analysis / / Robert Magnus |
| Autore | Magnus Robert |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] |
| Descrizione fisica | 1 online resource (258 pages) |
| Disciplina | 514.32 |
| Collana | Springer undergraduate mathematics series |
| Soggetto topico |
Metric spaces
Mathematics Espais mètrics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030949464
9783030949457 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Preliminaries on Sets -- Basic Relations -- Basic Operations -- Writing Predicates -- Set-Building Rules -- Relations and Functions -- Cardinals -- Other Notions -- 1 Metric Spaces -- 1.1 Metrics -- 1.1.1 Rationale for Metrics -- 1.1.2 Defining Metric Space -- 1.1.3 Exercises -- 1.2 Examples of Metric Spaces -- 1.2.1 Normed Spaces -- 1.2.2 Subspaces -- 1.2.3 Examples -- Not Subspaces of Normed Spaces -- 1.2.4 Pseudometrics -- 1.2.5 Cauchy-Schwarz, Hölder, Minkowski -- 1.2.6 Exercises -- 1.3 Cantor's Middle Thirds Set -- 1.3.1 Exercises -- 1.4 The Normed Spaces of Functional Analysis -- 1.4.1 Sequence Spaces -- 1.4.2 Function Spaces -- 1.4.3 Spaces of Continuous Functions -- 1.4.4 Spaces of Integrable Functions -- 1.4.5 Hölder's and Minkowski's Inequalities for Integrals -- 1.4.6 Exercises -- 2 Basic Theory of Metric Spaces -- 2.1 Balls in a Metric Space -- 2.1.1 Limit of a Convergent Sequence -- 2.1.2 Uniqueness of the Limit -- 2.1.3 Neighbourhoods -- 2.1.4 Bounded Sets -- 2.1.5 Completeness -- a Key Concept -- 2.1.6 Exercises -- 2.2 Open Sets, and Closed -- 2.2.1 Open Sets -- 2.2.2 Union and Intersection of Open Sets -- 2.2.3 Closed Sets -- 2.2.4 Union and Intersection of Closed Sets -- 2.2.5 Characterisation of Open and Closed Sets by Sequences -- 2.2.6 Interior, Closure and Boundary -- 2.2.7 Limit Points of Sets -- 2.2.8 Characterisation of Closure by Limit Points -- 2.2.9 Subspaces -- 2.2.10 Open and Closed Sets in a Subspace -- 2.2.11 Exercises -- 2.3 Continuous Mappings -- 2.3.1 Defining Continuity -- 2.3.2 New Views of Continuity -- 2.3.3 Limits of Functions -- 2.3.4 Characterising Continuity by Sequences -- 2.3.5 Lipschitz Mappings -- 2.3.6 Examples of Continuous Functions -- 2.3.7 Exercises -- 2.4 Continuity of Linear Mappings -- 2.4.1 Continuity Criterion -- 2.4.2 Operator Norms -- 2.4.3 Exercises.
2.5 Homeomorphisms and Topological Properties -- 2.5.1 Equivalent Metrics -- 2.5.2 Exercises -- 2.6 Topologies and σ-Algebras -- 2.6.1 Order Topologies -- 2.6.2 Exercises -- 2.6.3 Pointers to Further Study -- 2.7 () Mazur-Ulam -- 2.7.1 Exercises -- 3 Completeness of the Classical Spaces -- 3.1 Coordinate Spaces and Normed Sequence Spaces -- 3.1.1 Completeness of Rn -- 3.1.2 Completeness of p -- 3.1.3 Exercises -- 3.2 Product Spaces -- 3.2.1 Finitely Many Factors -- 3.2.2 Infinitely Many Factors -- 3.2.3 The Space 2N+ and the Cantor Set -- 3.2.4 Subspaces of Complete Spaces -- 3.2.5 Exercises -- 3.3 Spaces of Continuous Functions -- 3.3.1 Uniform Convergence -- 3.3.2 Series in Normed Spaces -- 3.3.3 The Weierstrass M-Test -- 3.3.4 The Spaces C(R) and Cp(R) -- 3.3.5 Exercises -- 3.4 () Rearrangements -- 3.4.1 Vector Series -- 3.4.2 Exercises -- 3.4.3 Pointers to Further Study -- 3.5 () Invertible Operators -- 3.5.1 Fredholm Integral Equation -- 3.5.2 Exercises -- 3.5.3 Pointers to Further Study -- 3.6 () Tietze -- 3.6.1 Formulas for an Extension -- 3.6.2 Exercises -- 3.6.3 Pointers to Further Study -- 4 Compact Spaces -- 4.1 Sequentially Compact Spaces -- 4.1.1 Continuous Functions on Sequentially Compact Spaces -- 4.1.2 Bolzano-Weierstrass in Rn -- 4.1.3 Sequentially Compact Sets in Rn -- 4.1.4 Sequentially Compact Sets in Other Spaces -- 4.1.5 The Space C(M) -- 4.1.6 Exercises -- 4.2 The Correct Definition of Compactness -- 4.2.1 Thoughts About the Definition -- 4.2.2 Compact Spaces and Compact Sets -- 4.2.3 Continuous Functions on Compact Spaces -- 4.2.4 Uniform Continuity -- 4.2.5 Exercises -- 4.3 Equivalence of Compactness and Sequential Compactness -- 4.3.1 Relative Compactness -- 4.3.2 Local Compactness -- 4.3.3 Exercises -- 4.4 Finite Dimensional Normed Vector Spaces -- 4.4.1 Exercises -- 4.5 () Ascoli -- 4.5.1 Peano's Existence Theorem. 4.5.2 Exercises -- 4.5.3 Pointers to Further Study -- 5 Separable Spaces -- 5.1 Dense Subsets of a Metric Space -- 5.1.1 Defining a Vector-Valued Integral -- 5.1.2 Exercises -- 5.2 Separability -- 5.2.1 Second Countability -- 5.2.2 Exercises -- 5.3 () Weierstrass -- 5.3.1 Exercises -- 5.3.2 Pointers to Further Study -- 5.4 () Stone-Weierstrass -- 5.4.1 Exercises -- 5.4.2 Pointers to Further Study -- 6 Properties of Complete Spaces -- 6.1 Cantor's Nested Intersection Theorem -- Notes About Cantor's Theorem -- 6.1.1 Categories -- Thoughts About the Proof -- 6.1.2 Exercises -- 6.2 () Genericity -- 6.2.1 Exercises -- 6.2.2 Pointers to Further Study -- 6.3 () Nowhere Differentiability -- 6.3.1 Exercises -- 6.3.2 Pointers to Further Study -- 6.4 Fixed Points -- 6.4.1 Exercises -- 6.5 () Picard -- 6.5.1 Exercises -- 6.6 () Zeros -- 6.6.1 Exercises -- 6.6.2 Pointers to Further Study -- 6.7 Completion of a Metric Space -- 6.7.1 Other Ways to Complete a Metric Space -- 6.7.2 Exercises -- 7 Connected Spaces -- 7.1 Connectedness -- 7.1.1 Connected Sets -- 7.1.2 Rules for Connected Sets -- 7.1.3 Connected Subsets of R -- 7.1.4 Exercises -- 7.2 Continuous Mappings and Connectedness -- 7.2.1 Continuous Curves -- 7.2.2 Arcwise Connectedness -- 7.2.3 Exiting a Set -- 7.2.4 Exercises -- 7.3 Connected Components -- 7.3.1 Examples of Connected Components -- 7.3.2 Arcwise Connected Components -- 7.3.3 Exercises -- 7.4 () Peano -- 7.4.1 Exercises -- 7.4.2 Pointers to Further Study -- Afterword -- Index. |
| Record Nr. | UNINA-9910553070403321 |
|
Magnus Robert
|
||
| Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||