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.
Sprache
Verlagsort
ISBN-13
978-0-486-17464-8 (9780486174648)
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Schweitzer Klassifikation
I. Introductory
II. Solution of Integral Equation of Second Kind by Successive Substitutions
III. Solution of Fredholm's Equation Expressed as Ratio of Two Integral Series in Lambda
IV. 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 Problem
V. 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 Equation
VI. 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 Bar
Index
