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13.2-5. The Characteristic Equation With Hilbert Kernel
13.2-6. The Tricomi Equation
13.3. Complete Singular Integral Equations Solvable in a Closed Form
13.3-1. Closed-Form Solutions in the Case of Constant Coefficients
13.3-2. Closed-Form Solutions in the General Case
13.4. The Regularization Method for Complete Singular Integral Equations
13.4-1. Certain Properties of Singular Operators
13.4-2. The Regularizer
13.4-3. The Methods of Left and Right Regularization
13.4-4. The Problem of Equivalent Regularization
13.4-5. Fredholm Theorems
13.4-6. The Carleman–Vekua Approach to the Regularization
13.4-7. Regularization in Exceptional Cases
13.4-8. The Complete Equation With Hilbert Kernel
14. Methods for Solving Nonlinear Integral Equations
14.1. Some Definitions and Remarks
14.1-1. Nonlinear Volterra Integral Equations
14.1-2. Nonlinear Equations With Constant Integration Limits
14.2. Nonlinear Volterra Integral Equations
14.2-1. The Method of Integral Transforms
14.2-2. The Method of Differentiation for Integral Equations
14.2-3. The Successive Approximation Method
14.2-4. The Newton–Kantorovich Method
14.2-5. The Collocation Method
14.2-6. The Quadrature Method
14.3. Equations With Constant Integration Limits
14.3-1. Nonlinear Equations With Degenerate Kernels
14.3-2. The Method of Integral Transforms
14.3-3. The Method of Differentiating for Integral Equations
14.3-4. The Successive Approximation Method
14.3-5. The Newton–Kantorovich Method
14.3-6. The Quadrature Method
14.3-7. The Tikhonov Regularization Method

Supplements
Supplement 1. Elementary Functions and Their Properties
1.1. Trigonometric Functions
1.2. Hyperbolic Functions
1.3. Inverse Trigonometric Functions
1.4. Inverse Hyperbolic Functions
Supplement 2. Tables of Indefinite Integrals
2.1. Integrals Containing Rational Functions
2.2. Integrals Containing Irrational Functions
2.3. Integrals Containing Exponential Functions
2.4. Integrals Containing Hyperbolic Functions
2.5. Integrals Containing Logarithmic Functions

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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