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Chapter 2: Methods for Second?Order Linear Differential Equations
- Homogeneous Linear Equations
- Nonhomogeneous Linear Equations
- Representation of Solutions as a Series in the Independent Variable
- Equation Coefficients are Representable in the Ordinary Power Series Form
- Equation Coefficients Have Poles at Some Point
- Asymptotic Solutions
- Boundary Value Problems. Green’s Function
- First, Second, Third, and Some Other Boundary Value Problems
- Simplification of Boundary Conditions. Self?Adjoint Form of Equations
- Green’s and Modified Green’s Functions. Representation Solutions via Green’s or Modified Green’s Functions
- Eigenvalue Problems
- Sturm?Liouville Problem
- General Properties of the Sturm-Liouville Problem (2.6.1.1), (2.6.1.2)
- Problems with Boundary Conditions of the First Kind
- Problems with Boundary Conditions of the Second Kind
- Problems with Boundary Conditions of the Third Kind
- Problems with Mixed Boundary Conditions
- Theorems on Estimates and Zeros of Solutions
- Theorem on Estimates of Solutions
- Sturm Comparison Theorem on Zeros of Solutions
- Qualitative Behavior of Solutions as x → ∞
- Numerical Methods
Abstract
? General form of a homogeneous linear equation.
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