Polyteknisk Boghandel

This book describes and analyses numerical methods for error analysis, differentiation, integration, interpolation and approximation, and the solution of non-linear equations, linear systems of algebraic equations and systems of ordinary differential equations.

Principles and algorithms are illustrated by examples in MATLAB. At the end of each chapter questions on theory and computer exercises are given.

Preface
Introduction
Matehematical Models and Numerical Approximations
Numerical Computation
References
Error Analysis and Computer Arithmetic
Sources of Error
Basic Concepts
Error Propagation
Number Representation
Rounding Errors in Floating Point
Arithmetic Operations in Floating Point
Accumulated Errors
IEEE Standard
Exercises
Computer Exercises
References
Function Evaluation
Introduction
Remainder Term Estimates
Standard Functions
Range Reduction
Trigonometric Functions
Nonlinear Equations
Introduction
Crude Localization
Iteration Methods
Convergence Analysis
Error Estimation and StoppingCriteria
Algebraic Equations
Square Root
Nonlinear Systems
Exercises
Computer Exercises
References
Interpolation
Introduction
Interpolation by Polynomials
Linear Interpolation
Newtons Interpolation Formula
Nevilles Method
Lagrange Interpolation
Hermite Interpolation
Runges Phenomenon
Splines
Linear Spline Functions
Cubic Splines
Cubic B-Splines
Exercises
Computer Exercises
References
Differentiation and Rchardson Extrapolation
Introduction
Difference Approximations
Difference Approcimaion Errors
Richardson Extrapolation
Exercises
Computer Exercises
References
Integration
Introduction
Trapezoidal Rule
Newton-Cotes Formulas
Rombergs Method
Difficulties with Numerical Integration
Adaptive Quadrature
Exercises
Computer Exercises
References
Linear Systems of Equations
Introduction
Triangular Systems
Gaussian Elimination
Pivoting
Permutations, Gauss Transformations
LU Factorization
Symmetric, Positive Definite Matrices
Band Matrices
Inverse Matrix
Vector and Matrix Norms
Sensitivity Analysis
Rounding Errors
Estimation of Condition Number
Overdetermined Systems
QR Factorization
Exercises
Computer Exercises
References
Approximation
Introduction
Important Concepts
Least Squares Method
Orthogonal Functions
Orthogonal Polynomials
Legendre Polynomials
Chebyshev Polynomials
Discree Cosine Transform
Minimax Approximation
Exercises
Computer Exercises
References
Ordinary Differential Equations
Introduction
Initial Value Problems
Local and Global Error
Runge-Kutta Methods
An Implicit Method
Stability
Adaptive Step Length Control
Boundary Value Problems
A Difference Method
A Finite Element Method
The Shooting Method
Exercises
Computer Exercises
References
Short Biographies
Answers to Exercises
Index