Principles of differential and integral equations /
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| Author / Creator: | Corduneanu, C. |
|---|---|
| Edition: | 2d ed. |
| Imprint: | Bronx, N.Y. : Chelsea Pub. Co., c1977. |
| Description: | xii, 205 p. ; 24 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/151369 |
Table of Contents:
- Introduction: Some Elementary Methods: The linear equation of the first order
- The equation with separable variables Exact differential equations
- The uniqueness problem: an example Some integral inequalities Problems
- 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 Problems Some Global Problems for Ordinary Differential
- Equations: Statement of the problems Global uniqueness Global existence and the behavior of saturated solutions
- Dependence of solutions on initial values Differential inequalities and the comparison method
- A criterion of global existence Problems Some Special Classes of Differential
- Systems and Equations: Linear systems: generalities Linear homogeneous systems Nonhomogeneous systems
- Linear equations of higher order Autonomous systems Linear systems and equations with constant coefficients Problems
- Stability Theory of Ordinary Differential Systems: Definitions and examples Stability of linear systems Stability in the first approximation
- Stability theorems by comparison method Further stability results Stability of automatic control systems Problems
- Volterra Integral Equations: Existence and uniqueness of solution An existence theorem
- The linear equation The first-kind linear equation Some problems on the half-axis Problems
- Fredholm Theory of Linear Integral Equations: The resolvent kernel
- The entire functions of Fredholm and their applications
- A glimpse of Hilbert space theory Eigenvalues, eigenfunctions and adjoint equations Problems
- Theory of Self-Adjoint Integral Equations and Some Applications: 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 Problems
- Miscellanea (Nice Things): Maximum and minimum solutions of scalar differential equations
- A theorem of Massera An oscillation theorem A formula of Picone and its consequences
- Lienard's equation Differential systems without uniqueness Abel's integral equation
- References
- Index