**Table of Contents** Preface / Computation in Fortran: Calculators and Computers / Errors in Computing / Complexity of Algorithms / Elements of FORTRAN / Equations: Real Roots / The General Iteration Method / Rate of Convergence / Convergence Theorems / Complex Roots / Algebraic Equations / Choice of Method / System of Equations: Linear System of Equations / Error: Matrix Norms and Condition Number / Relaxation Methods / Nonlinear System of Equations / Interpolation: Polynomial Interpolation / Equally Spaced Points: Finite Differences / Best Interpolation Nodes: Chebyshev Interpolation / Piecewise – Polynomial Spline Interpolation / Differentiation and Integration: Numerical Differentiation / Numerical Integration / Euler-Maclaurin Summation Formula / Improper Integrals / Double Integration / Ordinary Differential Equations: Initial Value Problem for First Order ODE / System of ODEs / Stiff Differential Equations / Boundary Value Problems / Partial Differential Equations: First Order Equation / The Diffusion Equation / The Wave Equation / Poisson Equation / Diffusion and Wave Equations in Two Dimension / Convergence: Lax’s Equivalence Theorem / Approximation: Uniform Approximation by Polynomials / Best Uniform (Minimax) Approximation / Least Squares Approximation / Orthogonal Polynomials / Orthogonal Polynomials Over Discrete Set of Points: Smoothing of Data / Trigonometric Approximation / Rational Approximations / Matrix Eigenvalues: General Theorems / Real Symmetric Matrices / General Matrices / Maximum Modulus Eigenvalue: The Power Method / The Characteristic Equation / Fast Fourier Transform: Discrete Fourier Transform / Fast Fourier Transform / FFT for N = r1r2…rm / Bibliography / Index.
**Audience**
Undergraduate – Postgraduate Students, Professionals & Researchers |