Principles of differential and integral equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
The Bronx, NY
Chelsea Publ. Co.
1977
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 205 S. |
| ISBN: | 0828402957 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Titel: Principles of differential and integral equations
Autor: Corduneanu, Constantin
Jahr: 1977
Contents Introduction 1. Some Elementary Methods The Linear Equation of the First Order 1 The Equation with Separable Variables ! Exact Differential Equations I The Uniqueness Problem: An Example | Some Integral Inequalities i Problems 2. Existence Theory for Differential Equations The First-Order Equation | First-Order Differential Systems Equations and Systems of Higher Order ! Peano Existence Theorem | A Uniqueness Theorem j Problems 3. Some Global Problems for Ordinary Differential Equations Statement of the Problems I Global Uniqueness I Global Existence and the Behavior of Saturated Solutions i Dependence of Solutions on Initial Values | Differential Inequalities and the Comparison Method | A Criterion of Global Existence i Problems
Contents xii 4 . Some Special Classes of Differential Systems and Equations 57 Linear Systems: Generalities | Linear Homogeneous Systems I Nonhomogeneous Systems | Linear Equations of Higher Order | Autonomous Systems | Linear Systems and Equations with Constant Coefficients | Problems 5 . Stability Theory of Ordinary Differential Systems 85 Definitions and Examples | Stability of Linear Systems I Stability in the First Approximation | Stability Theorems by Comparison Method | Further Stability Results | Stability of Automatic Control Systems | Problems 6. Volterra Integral Equations 119 Existence and Uniqueness of Solution I An Existence Theorem I The Linear Equation | The First-Kind Linear Equation I Some Problems on the Half-Axis | Problems 7 . Fredholm Theory of Linear Integral Equations 133 The Resolvent Kernel | The Entire Functions of Fredholm and Their Applications | A Glimpse of Hilbert Space Theory I Eigenvalues, Eigenfunctions and Adjoint Equations | Problems 8. Theory of Self-Adjoint Integral Equations and Some Applications 155 Some Properties of an Integral Operator | The Existence of Eigenvalues | The Hilbert-Schmidt Expansion Theorem | Complete Kernels and Systems | The Sturm-Liouville Problem | Reduction to an Integral Equation: The First Case | Reduction to an Integral Equation: The Second Case 1 Problems 9 . Miscellanea (Nice Things) 173 Maximum and Minimum Solutions of Scalar Differential Equations | A Theorem of Massera | An Oscillation Theorem I A Formula of Picone and Its Consequences | Liénard’s Equation | Differential Systems Without Uniqueness | Abel’s Integral Equation References 195 Index 203
|
| adam_txt |
Titel: Principles of differential and integral equations
Autor: Corduneanu, Constantin
Jahr: 1977
Contents Introduction 1. Some Elementary Methods The Linear Equation of the First Order 1 The Equation with Separable Variables ! Exact Differential Equations I The Uniqueness Problem: An Example | Some Integral Inequalities i Problems 2. Existence Theory for Differential Equations The First-Order Equation | First-Order Differential Systems Equations and Systems of Higher Order ! Peano Existence Theorem | A Uniqueness Theorem j Problems 3. Some Global Problems for Ordinary Differential Equations Statement of the Problems I Global Uniqueness I Global Existence and the Behavior of Saturated Solutions i Dependence of Solutions on Initial Values | Differential Inequalities and the Comparison Method | A Criterion of Global Existence i Problems
Contents xii 4 . Some Special Classes of Differential Systems and Equations 57 Linear Systems: Generalities | Linear Homogeneous Systems I Nonhomogeneous Systems | Linear Equations of Higher Order | Autonomous Systems | Linear Systems and Equations with Constant Coefficients | Problems 5 . Stability Theory of Ordinary Differential Systems 85 Definitions and Examples | Stability of Linear Systems I Stability in the First Approximation | Stability Theorems by Comparison Method | Further Stability Results | Stability of Automatic Control Systems | Problems 6. Volterra Integral Equations 119 Existence and Uniqueness of Solution I An Existence Theorem I The Linear Equation | The First-Kind Linear Equation I Some Problems on the Half-Axis | Problems 7 . Fredholm Theory of Linear Integral Equations 133 The Resolvent Kernel | The Entire Functions of Fredholm and Their Applications | A Glimpse of Hilbert Space Theory I Eigenvalues, Eigenfunctions and Adjoint Equations | Problems 8. Theory of Self-Adjoint Integral Equations and Some Applications 155 Some Properties of an Integral Operator | The Existence of Eigenvalues | The Hilbert-Schmidt Expansion Theorem | Complete Kernels and Systems | The Sturm-Liouville Problem | Reduction to an Integral Equation: The First Case | Reduction to an Integral Equation: The Second Case 1 Problems 9 . Miscellanea (Nice Things) 173 Maximum and Minimum Solutions of Scalar Differential Equations | A Theorem of Massera | An Oscillation Theorem I A Formula of Picone and Its Consequences | Liénard’s Equation | Differential Systems Without Uniqueness | Abel’s Integral Equation References 195 Index 203 |
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| isbn | 0828402957 |
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| spelling | Corduneanu, Constantin Verfasser aut Principles of differential and integral equations C. Corduneanu 2. ed. The Bronx, NY Chelsea Publ. Co. 1977 205 S. txt rdacontent n rdamedia nc rdacarrier Équations différentielles Équations intégrales Differential equations Integral equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Differentialgleichung (DE-588)4012249-9 s DE-604 Integralgleichung (DE-588)4027229-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015151254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Corduneanu, Constantin Principles of differential and integral equations Équations différentielles Équations intégrales Differential equations Integral equations Differentialgleichung (DE-588)4012249-9 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4027229-1 (DE-588)4151278-9 |
| title | Principles of differential and integral equations |
| title_auth | Principles of differential and integral equations |
| title_exact_search | Principles of differential and integral equations |
| title_exact_search_txtP | Principles of differential and integral equations |
| title_full | Principles of differential and integral equations C. Corduneanu |
| title_fullStr | Principles of differential and integral equations C. Corduneanu |
| title_full_unstemmed | Principles of differential and integral equations C. Corduneanu |
| title_short | Principles of differential and integral equations |
| title_sort | principles of differential and integral equations |
| topic | Équations différentielles Équations intégrales Differential equations Integral equations Differentialgleichung (DE-588)4012249-9 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Équations différentielles Équations intégrales Differential equations Integral equations Differentialgleichung Integralgleichung Einführung |
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