Table of Contents:
Analysis Versus Numerical Analysis
- Computers and Numerical Analysis
- An Illustrative Example
- Kinds of Errors in Numerical Procedures
- Interval Arithmetic
- Parallel and Distributed Computing
- Measuring the Efficiency of Numerical Procedures
- Exercises
- Applied Problems and Projects
Solving Nonlinear Equations
- Interval Halving (Bisection)
- Linear Interpolation Methods
- Newton's Method
- Muller's Method
- Fixed-Point Iteration: x = g(x) Method
- Multiple Roots
- Nonlinear Systems
- Exercises
- Applied Problems and Projects
Solving Sets of Equations
- Matrices and Vectors
- Elimination Methods
- The Inverse of a Matrix and Matrix Pathology
- Ill-Conditioned Systems
- Iterative Methods
- Parallel Processing
- Exercises
- Applied Problems and Projects
Interpolation and Curve Fitting
- Interpolating Polynomials
- Divided Differences
- Spline Curves
- Bezier Curves and B-Splines Curves
- Interpolating on a Surface
- Least-Squares Approximations
- Exercises
- Applied Problems and Projects
Approximation of Functions
- Chebyshev Polynomials and Chebyshev Series
- Rational Function Approximations
- Fourier Series
- Exercises
- Applied Problems and Projects
Numerical Differentiation and Integration
- Differentiation with a Computer
- Numerical Integration-The Trapezoidal Rule
- Simpson's Rules
- An Application of Numerical Integration-Fourier Series and Fourier Transforms
- Adaptive Integration
- Gaussian Quadrature
- Multiple Integrals
- Applications of Cubic Splines
- Exercises
- Applied Problems and Projects
Numerical Solution of Ordinary
- Differential Equations
- The Taylor-Series Method
- The Euler Method and Its Modifications
- Runge-Kutta Methods
- Multistep Methods
- Higher-Order Equations and Systems
- Stiff Equations
- Boundary-Value Problems
- Characteristic-Value Problems
- Exercises
- Applied Problems and Projects
Optimization
- Finding the Minimum of y = f(x)
- Minimizing a Function of Several Variables
- Linear Programming
- Nonlinear Programming
- Other Optimizations
- Exercises
- Applied Problems and Projects
Partial-Differential Equations
- Elliptic Equations
- Parabolic Equations
- Hyperbolic Equations
- Exercises
- Applied Problems and Projects
Finite Element Analysis
- Mathematical Background
- Finite Elements for Ordinary-Differential Equations
- Finite Elements for Partial-Differential Equations
- Exercises
- Applied Problems and Projects
Appendixes
- A Some Basic Information from Calculus
- B Software Resources
- Answers to Selected Exercises
- References
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