1. The Analytic Theory of Differential Equations.- ???1. Analyticity of the Solutions of a System of Ordinary Differential Equations.- ??? 2. Regular Singular Points.- ??? 3. Irregular Singular Points.- 2. Second-Order Equations on the Real Line.- ??? 1. Transformations of Second-Order Equations.- ??? 2. WKB-Bounds.- ??? 3. Asymptotic Behaviour of Solutions of a Second-Order Equation for Large Values of the Parameter.- ??? 4. Systems of Two Equations Containing a Large Parameter.- ??? 5. Systems of Equations Close to ...
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1. The Analytic Theory of Differential Equations.- ???1. Analyticity of the Solutions of a System of Ordinary Differential Equations.- ??? 2. Regular Singular Points.- ??? 3. Irregular Singular Points.- 2. Second-Order Equations on the Real Line.- ??? 1. Transformations of Second-Order Equations.- ??? 2. WKB-Bounds.- ??? 3. Asymptotic Behaviour of Solutions of a Second-Order Equation for Large Values of the Parameter.- ??? 4. Systems of Two Equations Containing a Large Parameter.- ??? 5. Systems of Equations Close to Diagonal Form.- ??? 6. Asymptotic Behaviour of the Solutions for Large Values of the Argument.- ??? 7. Dual Asymptotic Behaviour.- ??? 8. Counterexamples.- ??? 9. Roots of Constant Multiplicity.- ??? 10. Problems on Eigenvalues.- ??? 11. A Problem on Scattering.- 3. Second-Order Equations in the Complex Plane.- ??? 1. Stokes Lines and the Domains Bounded by them.- ??? 2. WKB-Bounds in the Complex Plane.- ??? 3. Equations with Polynomial Coefficients. Asymptotic Behaviour of a Solution in the Large.- ??? 4. Equations with Entire or Meromorphic Coefficients.- ??? 5. Asymptotic Behaviour of the Eigenvalues of the Operator -d2 / dx2 + ?2q(x). Self-Adjoint Problems.- ??? 6. Asymptotic Behaviour of the Discrete Spectrum of the Operator -y? + ?2q(x)y. Non-Self-Adjoint Problems.- ??? 7. The Eigenvalue Problem with Regular Singular Points.- ??? 8. Quasiclassical Approximation in Scattering Problems.- ??? 9. Sturm-Liouville Equations with Periodic Potential.- 4. Second-Order Equations with Turning Points.- ??? 1. Simple Turning Points. The Real Case.- ??? 2. A Simple Turning Point. The Complex Case.- ??? 3. Some Standard Equations.- ???4. Multiple and Fractional Turning Points.- ??? 5. The Fusion of a Turning Point and Regular Singular Point.- ??? 6. Multiple Turning Points. The Complex Case.- ??? 7. Two Close Turning Points.- ??? 8. Fusion of Several Turning Points.- 5. nth-Order Equations and Systems.- ??? 1. Equations and Systems on a Finite Interval.- ??? 2. Systems of Equations on a Finite Interval.- ??? 3. Equations on an Infinite Interval.- ??? 4. Systems of Equations on an Infinite Interval.- ??? 5. Equations and Systems in the Complex Plane.- ??? 6. Turning Points.- ??? 7. A Problem on Scattering, Adiabatic Invariants and a Problem on Eigenvalues.- ??? 8. Examples.- References.
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