Author | Fedoryuk, Mikhail V. author |
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Title | Asymptotic Analysis [electronic resource] : Linear Ordinary Differential Equations / by Mikhail V. Fedoryuk |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993 |
Connect to | http://dx.doi.org/10.1007/978-3-642-58016-1 |
Descript | VIII, 363 p. online resource |
1. The Analytic Theory of Differential Equations -- ยง1. Analyticity of the Solutions of a System of Ordinary Differential Equations -- ยง 2. Regular Singular Points -- ยง 3. Irregular Singular Points -- 2. Second-Order Equations on the Real Line -- ยง 1. Transformations of Second-Order Equations -- ยง 2. WKB-Bounds -- ยง 3. Asymptotic Behaviour of Solutions of a Second-Order Equation for Large Values of the Parameter -- ยง 4. Systems of Two Equations Containing a Large Parameter -- ยง 5. Systems of Equations Close to Diagonal Form -- ยง 6. Asymptotic Behaviour of the Solutions for Large Values of the Argument -- ยง 7. Dual Asymptotic Behaviour -- ยง 8. Counterexamples -- ยง 9. Roots of Constant Multiplicity -- ยง 10. Problems on Eigenvalues -- ยง 11. A Problem on Scattering -- 3. Second-Order Equations in the Complex Plane -- ยง 1. Stokes Lines and the Domains Bounded by them -- ยง 2. WKB-Bounds in the Complex Plane -- ยง 3. Equations with Polynomial Coefficients. Asymptotic Behaviour of a Solution in the Large -- ยง 4. Equations with Entire or Meromorphic Coefficients -- ยง 5. Asymptotic Behaviour of the Eigenvalues of the Operator -d2 / dx2 + ?2q(x). Self-Adjoint Problems -- ยง 6. Asymptotic Behaviour of the Discrete Spectrum of the Operator -y? + ?2q(x)y. Non-Self-Adjoint Problems -- ยง 7. The Eigenvalue Problem with Regular Singular Points -- ยง 8. Quasiclassical Approximation in Scattering Problems -- ยง 9. Sturm-Liouville Equations with Periodic Potential -- 4. Second-Order Equations with Turning Points -- ยง 1. Simple Turning Points. The Real Case -- ยง 2. A Simple Turning Point. The Complex Case -- ยง 3. Some Standard Equations -- ยง4. Multiple and Fractional Turning Points -- ยง 5. The Fusion of a Turning Point and Regular Singular Point -- ยง 6. Multiple Turning Points. The Complex Case -- ยง 7. Two Close Turning Points -- ยง 8. Fusion of Several Turning Points -- 5. nth-Order Equations and Systems -- ยง 1. Equations and Systems on a Finite Interval -- ยง 2. Systems of Equations on a Finite Interval -- ยง 3. Equations on an Infinite Interval -- ยง 4. Systems of Equations on an Infinite Interval -- ยง 5. Equations and Systems in the Complex Plane -- ยง 6. Turning Points -- ยง 7. A Problem on Scattering, Adiabatic Invariants and a Problem on Eigenvalues -- ยง 8. Examples -- References