Author | Stenger, Frank. author |
---|---|
Title | Numerical Methods Based on Sinc and Analytic Functions [electronic resource] / by Frank Stenger |
Imprint | New York, NY : Springer New York, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2706-9 |
Descript | XV, 565p. 8 illus. online resource |
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 RiemannโHilbert 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 PaleyโWiener 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 ? -- Problems for 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