Book:Richard W. Hamming/Numerical Methods for Scientists and Engineers

Subject Matter

 * Numerical Analysis

Contents

 * Preface


 * I Fundamentals and Algorithms


 * 1 An Essay on Numerical Methods
 * 2 Numbers
 * 3 Function Evaluation
 * 4 Real Zeros
 * 5 Complex Zeros
 * *6 Zeros of Polynomials
 * 7 Linear Equations and Matrix Inversion
 * *8 Random Numbers
 * 9 The Difference Calculus
 * 10 Roundoff
 * *11 The Summation Calculus
 * *12 Infinite Series
 * 13 Difference Equations


 * II Polynomial Approximation - Classical Theory
 * 14 Polynomial Interpolation
 * 15 Formulas Using Function Values
 * 16 Error Terms
 * 17 Formulas Using Derivatives
 * 18 Formulas Using Differences
 * *19 Formulas Using the Sample Points as Parameters
 * 20 Composite Formulas
 * 21 Indefinite Integrals - Feedback
 * 22 Introduction to Differential Equations
 * 23 A General Theory of Predictor-Corrector Methods
 * 24 Special Methods of Integrating Ordinary Differential Equations
 * 25 Least Squares: Theory
 * 26 Orthogonal Functions
 * 27 Least Squares: Practice
 * 28 Chebyshev Approximation: Theory
 * 29 Chebyshev Approximation: Practice
 * *30 Rational Function Approximation


 * III Fourier Approximation - Modern Theory
 * 31 Fourier Series: Periodic Functions
 * 32 Convergence of Fourier Series
 * 33 The Fast Fourier Transform
 * 34 The Fourier Integral: Nonperiodic Functions
 * 35 A Second Look at Polynomial Approximation - Filters
 * *36 Integrals and Differential Equations
 * *37 Design of Digital Filters
 * *38 Quantization of Signals


 * IV Exponential Approximation
 * 39 Sums of Exponentials
 * *40 The Laplace Transform
 * *41 Simulation and the Method of Zeros and Poles


 * V Miscellaneous
 * 42 Approximations to Singularities
 * 43 Optimization
 * 44 Linear Independence
 * 45 Eigenvalues and Eigenvectors of Hermitian Matrices
 * $$N + 1$$ The Art of Computing for Scientists and Engineers


 * Index


 * Starred sections may be omitted.