Linear Integral Equations (eBook)

William Vernon Lovitt (Autor)

eBook Download: EPUB

2014
272 Seiten
Dover Publications (Verlag)
978-0-486-17464-8 (ISBN)

Infos

Not only general theory of linear equations but also differential equations, calculus of variations, and special areas in mathematical physics. Discusses Fredholm’s equation, Hilbert-Schmidt theory, and auxiliary theorems on harmonic functions. 1924 edition.

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Readable and systematic, this volume offers coherent presentations of not only the general theory of linear equations with a single integration, but also of applications to differential equations, the calculus of variations, and special areas in mathematical physics. Topics include the solution of Fredholm’s equation expressed as a ratio of two integral series in lambda, free and constrained vibrations of an elastic string, and auxiliary theorems on harmonic functions. Discussion of the Hilbert-Schmidt theory covers boundary problems for ordinary linear differential equations, vibration problems, and flow of heat in a bar. 1924 edition.

Inhalt

I. IntroductoryII. Solution of Integral Equation of Second Kind by Successive SubstitutionsIII. Solution of Fredholm’s Equation Expressed as Ratio of Two Integral Series in LambdaIV. Applications of the Fredholm Theory I. Free Vibrations of an Elastic String II. Constrained Vibrations of an Elastic String III. Auxiliary Theorems on Harmonic Functions IV. Logarithmic Potential of a Double Layer V. Fredholm’s Solution of Dirichlet’s Problem VI. Logarithmic Potential of a Simple Layer VII. Fredholm’s Solution of Neumann’s ProblemV. Hilbert-Schmidt Theory of Integral Equations with Symmetric Kernels I. Existence of at Least One Characteristic Constant II. Orthogonality III. Expansion of an Arbitrary Function According to the fundamental functions of a Complete Normalized Orthogonal System IV. Expansion of the Kernel According to the Fundamental Functions of a Complete Normalized Orthogonal System V. Auxiliary Theorems VI. Solution of the Integral EquationVI. Applications of the Hilbert-Schmidt Theory I. Boundary Problems for Ordinary Linear Differential Equations II. Applications to Some Problems of the Calculus of Variations III. Vibration Problems IV. Applications of the Hilbert-Schmidt Theory of the Flow of Heat in a BarIndex

Produkt-Details

• Erscheint lt. Verlag: 5.3.2014
• Reihe/Serie: Dover Books on Physics
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 476 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 0-486-17464-6 / 0486174646
• ISBN-13: 978-0-486-17464-8 / 9780486174648