Approximation Techniques for Engineers : Second Edition

Content: Cover
 Half Title
 Title Page
 Copyright Page
 Contents
 Preface to the second edition
 Preface
 Acknowledgments
 About the author
 I: Data approximations
 1 Classical interpolation methods
 1.1 Newton interpolation
 1.1.1 Equidistant Newton interpolation
 1.1.2 Computational example
 1.2 Lagrange interpolation
 1.2.1 Equidistant Lagrange interpolation
 1.2.2 Computational example
 1.2.3 Parametric Lagrange interpolation
 1.3 Hermite interpolation
 1.3.1 Computational example
 1.4 Interpolation of functions of two variables with polynomials
 References
 2 Approximation with splines 2.1 Natural cubic splines2.1.1 Equidistant natural spline approximation
 2.1.2 Computational example
 2.2 Bezier splines
 2.2.1 Rational Bezier splines
 2.2.2 Computational example
 2.3 Approximation with B-splines
 2.3.1 Computational example
 2.3.2 Nonuniform B-splines
 2.3.3 Nonuniform rational B-splines
 2.4 Surface spline approximation
 2.4.1 Coons surfaces
 2.4.2 Computational example
 2.4.3 Bezier surfaces
 2.4.4 Triangular surface patches
 2.4.5 Computational example
 References
 3 Least squares approximation
 3.1 The least squares principle
 3.2 Linear least squares approximation 3.3 Polynomial least squares approximation3.4 Computational example
 3.5 Exponential and logarithmic least squares approximations
 3.6 Nonlinear least squares approximation
 3.6.1 Computational example
 3.7 Trigonometric least squares approximation
 3.7.1 Computational example
 3.8 Directional least squares approximation
 3.9 Weighted least squares approximation
 References
 4 Approximation of functions
 4.1 Least squares approximation of functions
 4.2 Approximation with Legendre polynomials
 4.2.1 Gram-Schmidt orthogonalization
 4.2.2 Computational example
 4.3 Chebyshev approximation 4.3.1 Collapsing a power series4.3.2 Computational example
 4.4 Fourier approximation
 4.4.1 Computational example
 4.4.2 Complex Fourier approximation
 4.5 Padé approximation
 4.5.1 Computational example
 4.6 Approximating matrix functions
 4.6.1 Taylor series approximation of matrix functions
 References
 5 Numerical differentiation
 5.1 Finite difference formulae
 5.1.1 Three-point finite difference formulae
 5.1.2 Computational example
 5.2 Higher order derivatives
 5.3 Richardson extrapolation
 5.3.1 Computational example
 5.4 Multipoint finite difference formulae
 References 6 Numerical integration6.1 The Newton-Cotes class
 6.1.1 The trapezoid rule
 6.1.2 Simpson's rule
 6.1.3 Computational example
 6.1.4 Open Newton-Cotes formulae
 6.2 Advanced Newton-Cotes methods
 6.2.1 Composite methods
 6.2.2 Romberg's method
 6.2.3 Computational example
 6.3 Gaussian quadrature
 6.3.1 Computational example
 6.4 Integration of functions of multiple variables
 6.4.1 Gaussian cubature
 6.5 Chebyshev quadrature
 6.6 Numerical integration of periodic functions
 References
 II: Approximate solutions
 7 Nonlinear equations in one variable
 7.1 General equations