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High Quality Content by WIKIPEDIA articles! 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.Such values of ? when they exist are called the eigenvalues of the boundary value problem defined by (1) and the prescribed set of boundary conditions. The corresponding solutions (for such a ?) are the eigenfunctions of this problem. Under normal assumptions on the coefficient functions p(x), q(x), and w(x) above, they induce a Hermitian differential operator in some function space defined by boundary conditions. The resulting theory of the existence and asymptotic behavior of the eigenvalues, the corresponding qualitative theory of the eigenfunctions and their completeness in a suitable function space became known as Sturm?Liouville theory. This theory is important in applied mathematics, where S?L problems occur very commonly, particularly when dealing with linear partial differential equations that are separable. ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 1801 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more