Numerical methods

Suitable for upper-level undergraduate and graduate two-semester sequence courses, or for any of several different one-term courses, depending on course emphasis.

This text presents the fundamental numerical techniques used in engineering, applied mathematics, computer science, and the physical and life sciences in a manner that is both interesting and understandable. Each topic is illustrated by examples that range in complexity from very simple to moderate and are supported by geometrical or graphical illustrations where appropriate.

1. FOUNDATIONS.
Sample Problems and Numerical Methods.
Some Basic Issues.
Algorithms and Computer Programs.

2. SOLVING EQUATIONS OF ONE VARIABLE.
Bisection Method.
Regular Falsi and Secant Methods.
Newtons Method.
Mullers Method.
Methods of Modern Computing.

3. SOLVING SYSTEMS OF LINEAR EQUATIONS: DIRECT METHODS.
Gaussian Elimination.
Gaussian Elimination with Row Pivoting.
Gaussian Elimination for Tridiagonal Systems.
Methods of Modern Computing.

4. LU AND QR FACTORIZATION.
LU Factorization from Gaussian Elimination.
Direct LU Factorization. Applications of LU Factorization.
Householder and Givens Transformations.
QR Factorization.
Methods of Modern Computing.

5. EIGENVALUES AND EIGENVECTORS.
Power Method.
Inverse Power Method.
QR Method.
Methods of Modern Computing.

6. SOLVING SYSTEMS OF LINEAR EQUATIONS: ITERATIVE METHODS.
Jacobi Method.
Gauss-Seidel Method.
Successive Over Relaxation.
Methods of Modern Computing.

• Comprehensive coverage of a variety of topics in logical sequence - Including coverage of solving nonlinear equations of a single variable, numerical linear algebra, nonlinear functions of several variables, numerical methods for data interpolations and approximation, numerical differentiation and integration, and numerical techniques for solving differential equations.
• Brief introduction to the long history of numerical techniques - Found in Chapter 1.
  Provides students with the background knowledge necessary to progress through the rest of the text.
• Sample programs - Provided in several different languages.
• Overview of chapter content.
• Chapter-opening introductory examples, suggests several types of problems for which the chapter topics may be used.
• Chapte