1 Mathematical Preliminaries. - 1. 1 Properties of Analytic Functions. - Problems for Section 1. 1. - 1. 2 Hilbert Transforms. - Problems for Section 1. 2. - 1. 3 RiemannHilbert Problems. - Problems for Section 1. 3. - 1. 4 Fourier Transforms. - Problems for Section 1. 4. - 1. 5 Laplace Transforms. - Problems for Section 1. 5. - 1. 6 Fourier Series. - Problems for Section 1. 6. - 1. 7 Transformations of Functions. - Problems for Section 1. 7. - 1. 8 Spaces of Analytic Functions. - Problems for Section 1. 8. - 1. 9 The PaleyWiener Theorem. - Problems for Section 1. 9. - 1. 10 The Cardinal Function. - Problems for Section 1. 10. - Historical Remarks on Chapter 1. - 2 Polynomial Approximation. - 2. 1 Chebyshev Polynomials. - Problems for Section 2. 1. - 2. 2 Discrete Fourier Polynomials. - Problems for Section 2. 2. - 2. 3 The Lagrange Polynomial. - Problems for Section 2. 3. - 2. 4 Faber Polynomials. - Problems for Section 2. 4. - Historical Remarks on Chapter 2. - 3 Sinc Approximation in Strip. - 3. 1 Sinc Approximation in Dd. - Problems for Section 3. 1. - 3. 2 Sinc Quadrature on (?? ?). - Problems for Section 3. 2. - 3. 3 Discrete Fourier Transforms on (???). - Problems for Section 3. 3. - 3. 4 Cauchy-Like Transforms on (???). - Problems for Section 3. 4. - 3. 5 Approximation of Derivatives in Dd. - Problems for Section 3. 5. - 3. 6 The Indefinite Integral on (?? ?). - Problems for Section 3. 6. - Historical Remarks on Chapter 3. - 4 Sinc Approximation on ?. - 4. 1 Basic Definitions. - Problems for Section 4. 1. - 4. 2 Interpolation and Quadrature on ?. - Problems for Section 4. 2. - 4. 3 Hilbert and Related Transforms on ?. - Problems for Section 4. 3. - 4. 4 Approximation of Derivatives on ?. - Problems for Section 4. 4. - 4. 5 Indefinite Integral Over ?. - Problems for Section 4. 5. - 4. 6 Indefinite Convolution Over ?. - Problemsfor Section 4. 6. - Historical Remarks on Chapter 4. - 5 Sinc-Related Methods. - 5. 1 Introduction. - 5. 2 Variations of the Sinc Basis. - Problems for Section 5. 2. - 5. 3 Elliptic Function Interpolants. - Problems for Section 5. 3. - 5. 4 Inversion of the Laplace Transform. - Problems for Section 5. 4. - 5. 5 Sinc-Like Rational Approximation. - Problems for Section 5. 5. - 5. 6 Rationals and Extrapolation. - Problems for Section 5. 6. - 5. 7 Heaviside and Filter Rationals. - Problems for Section 5. 7. - 5. 8 Positive Base Approximation. - Problems for Section 5. 8. - Historical Remarks on Chapter 5. - 6 Integral Equations. - 6. 1 Introduction. - 6. 2 Mathematical Preliminaries. - Problems for Section 6. 2. - 6. 3 Reduction to Algebraic Equations. - Problems for Section 6. 3. - 6. 4 Volterra Integral Equations. - Problems for Section 6. 4. - 6. 5 Potential Theory Problems. - Problems for Section 6. 5. - 6. 6 Reduced Wave Equation on a Half-Space. - Problems for Section 6. 6. - 6. 7 Cauchy Singular Integral Equations. - Problems for Section 6. 7. - 6. 8 Convolution-Type Equations. - Problems for Section 6. 8. - 6. 9 The Laplace Transform and Its Inversion. - Problems for Section 6. 9. - Historical Remarks on Chapter 6. - 7 Differential Equations. - 7. 1 ODE-IVP. - Problems for Section 7. 1. - 7. 2 ODE-BVP. - Problems for Section 7. 2. - 7. 3 Analytic Solutions of PDE. - Problems for Section 7. 3. - 7. 4 Elliptic Problems. - Problems for Section 7. 4. - 7. 5 Hyperbolic Problems. - Problems for Section 7. 5. - 7. 6 Parabolic Problems. - Problems for Section 7. 6. - Historical Remarks on Chapter 7. - References. Language: English