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 ed.

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