Handbook of Integral Equations

EXACT SOLUTIONS OF INTEGRAL EQUATIONS Linear Equations of the First Kind with Variable Limit of Integration Linear Equations of the Second Kind with Variable Limit of Integration Linear Equations of the First Kind with Constant Limits of Integration Linear Equations of the Second Kind with Constant Limits of Integration Nonlinear Equations of the First Kind with Variable Limit of Integration Nonlinear Equations of the Second Kind with Variable Limit of Integration Nonlinear Equations of the First Kind with Constant Limits of Integration Nonlinear Equations of the Second Kind with Constant Limits of Integration METHODS FOR SOLVING INTEGRAL EQUATIONS Main Definitions and Formulas: Integral Transforms Methods for Solving Linear Equations of the Form xa K(x, t)y(t)dt = f(x) Methods for Solving Linear Equations of the Form y(x) - xa K(x, t)y(t)dt = f(x) Methods for Solving Linear Equations of the Form xa K(x, t)y(t)dt = f(x) Methods for Solving Linear Equations of the Form y(x) - xa K(x, t)y(t)dt = f(x) Methods for Solving Singular Integral Equations of the First Kind Methods for Solving Complete Singular Integral Equations Methods for Solving Nonlinear Integral Equations Methods for Solving Multidimensional Mixed Integral Equations Application of Integral Equations for the Investigation of Differential Equations SUPPLEMENTS Elementary Functions and Their Properties Finite Sums and Infinite Series Tables of Indefinite Integrals Tables of Definite Integrals Tables of Laplace Transforms Tables of Inverse Laplace Transforms Tables of Fourier Cosine Transforms Tables of Fourier Sine Transforms Tables of Mellin Transforms Tables of Inverse Mellin Transforms Special Functions and Their Properties Some Notions of Functional Analysis References Index