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# Sturm-Liouville theory.

0821839055

Sturm-Liouville theory In mathematics and its applications, a classical Sturm-Liouville equation, named after Jacques Charles François Sturm (1803-1855) and Joseph Liouville (1809-1882), is a real second-order linear differential equation of the form

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Zettl, Anton.

Amer. Mathematical Society

2005

328 pages

\$84.00

Hardcover

Mathematical surveys and monographs; v.121

QA379

Sturm and Liouville published a series of papers on second order linear ordinary differential equations ordinary differential equation

Equation containing derivatives of a function of a single variable. Its order is the order of the highest derivative it contains (e.g., a first-order differential equation involves only the first derivative of the function).
including boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions.  back in 1836-37, but the topic is still an area of intense activity today. This monograph is presented with the twin goals of providing a modern survey of the basic properties of the Sturm- Liouville equation and to introduce some aspects of recent research on Sturm-Liouville problems. Chapters cover first order systems, scalar scalar, quantity or number possessing only sign and magnitude, e.g., the real numbers (see number), in contrast to vectors and tensors; scalars obey the rules of elementary algebra. Many physical quantities have scalar values, e.g.  initial value problems, two-point regular boundary value problems, regular self-adjoint problems, regular left-definite and indefinite problems, oscillation Oscillation

Any effect that varies in a back-and-forth or reciprocating manner. Examples of oscillation include the variations of pressure in a sound wave and the fluctuations in a mathematical function whose value repeatedly alternates above and below some
, the limit-point/limit-circle dichotomy, singular initial value problem, two-point singular boundary value problems, singular self-adjoint problems, singular indefinite problems, singular left-definite problems, and examples.

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