Numerical Computing and Computers. Introduction.
Using a Computer to Do Numerical Analysis.
A Typical Example.
Implementing Bisection.
Computer Arithmetic and Errors.
Theoretical Matters.
Parallel and Distributed Computing.
Chapter Summary.
Exercises.
Solving Nonlinear Equations. Pressure Drop for a Flowing Fluid.
Interval Halving (Bisection) Revisited.
Linear Interpolation Methods.
Newton's Method.
Muller's Method.
Fixed-Point Iteration:
x = g(x) Method.
Newton's Method for Polynomials.
Bairstow's Method for Quadratic Factors.
Other Methods for Polynomials.
Multiple Roots.
Theoretical Matters.
Using MATLAB.
Chapter Summary.
Computer Programs.
Exercises.
Solving Sets of Equations. Applications of Sets of Equations.
Matrix Notation.
The Elimination Method.
Gaussian Elimination and Gauss-Jordan Methods.
Other Direct Methods.
Pathology in Linear Systems-Singular Matrices.
Determinants and Matrix Inversion.
Norms.
Condition Numbers and Errors in Solutions.
Iterative Methods.
Relaxation Method.
Systems of Nonlinear Equations.
Theoretical Matters.
Using Maple and MATLAB.
Parallel Processing.
Chapter Summary.
Computer Programs.
Exercises.
Interpolation and Curve Fitting. An Interpolation Problem.
Lagrangian Polynomials.
Divided Differences.
Interpolating with a Cubic Spline.
Bezier Curves and B-Spline Curves.
Polynomial Approximation of Surfaces.
Least-Squares Approximations.
Theoretical Matters.
Using MATLAB and Mathematica.
Chapter Summary.
Computer Programs.
Exercises.
Approximation of Functions. Chebyshev Polynomials.
Economized Power Series.
Approximation with Rational Functions.
Fourier Series.
Theoretical Matters.
Using Computer Algebra Systems.
Chapter Summary.
Computer Program.
Exercises.
Numerical Differentiation and Numerical Integration. Getting Derivatives and Integrals Numerically.
Derivatives from Difference Tables.
Higher-Order Derivatives.
Extrapolation Techniques.
Newton-Cotes Integration Formulas.
The Trapezoidal Rule-A Composite Formula.
Simpson's Rules.
Other Ways to Derive Integration Formulas.
Gaussian Quadrature.
Adaptive Integration.
Multiple Integrals.
Multiple Integration with Variable Limits.
Applications of Cubic Splines.
An Application of Numerical Integration-Fourier Transforms.
Theoretical Matters.
Using MATLAB.
Parallel Processing.
Chapter Summary.
Computer Programs.
Exercises.
Numerical Solution of Ordinary Differential Equations. The Spring-Mass Problem-A Variation.
Taylor-Series Method.
Euler and Modified Euler Methods.
Runge-Kutta Methods.
Multistep Methods.
Milne's Method.
Adams-Moulton Method.
Convergence Criteria.
Systems of Equations and Higher-Order Equations.
Comparison of Methods/Stiff Equations.
Theoretical Matters.
Using Maple and MATLAB.
Chapter Summary.
Computer Programs.
Exercises.
Boundary-Value Problems. Temperature Distribution in a Rod.
The Shooting Method.
Solution Through a Set of Equations.
Derivative Boundary Conditions.
Characteristic-Value Problems.
Temperature Distribution in a Slab.
Solving for the Temperatures in a Slab.
The Alternating Direction Implicit Method.
Irregular Regions and Nonrectangular Grids.
Theoretical Matters.
Using MATLAB.
Chapter Summary.
Computer Programming.
Parallel Processing.
Exercises.
Parabolic and Hyperbolic Partial-Differential Equations. Types of Partial-Differential Equations.
The Heat Equation and the Wave Equation.
Solution Techniques for the Heat Equation in One Dimension.
Solving the Vibrating String Problem.
Parabolic Equations in Two or Three Dimensions.
The Wave Equation in Two Dimensions.
Theoretical Matters.
Chapter Summary.
Computer Programs.
Exercises.
The Finite Element Method. The Rayleigh-Ritz Method.
Collocation and Galerkin Methods.
Finite Elements for an Ordinary-Differential Equation.
Finite Elements for an Elliptic Partial-Differential Equation.
Finite Elements for Parabolic and Hyperbolic Equations.
Theoretical Matters.
Chapter Summary.
Computer Program.
Exercises.
Appendices. Some Basic Information from Calculus.
Deriving Formulas by the Method of Undetermined Coefficients.
Software Resources. Answers to Selected Exercises. References. Index. 