Download PDF Numerical Analysis NINTH EDITION by Richard L. Burden

Sinopsis

This book was written for a sequence of courses on the theory and application of numerical approximation techniques. It is designed primarily for junior-level mathematics, science, and engineering majors who have completed at least the standard college calculus sequence. Familiarity with the fundamentals of linear algebra and differential equations is useful, but there is sufficient introductory material on these topics so that courses in these subjects are not needed as prerequisites.

The book contains sufficient material for at least a full year of study, but we expect many people to use it for only a single-term course. In such a single-term course, students learn to identify the types of problems that require numerical techniques for their solution and see examples of the error propagation that can occur when numerical methods are applied. They accurately approximate the solution of problems that cannot be solved exactly and learn typical techniques for estimating error bounds for the approximations. The remainder of the text then serves as a reference for methods not considered in the course. Either the full-year or single-course treatment is consistent with the philosophy of the text.

Virtually every concept in the text is illustrated by example, and this edition contains more than 2600 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory. In addition, the exercise sets include numerous applied problems from diverse areas of engineering as well as from the physical, computer, biological, economic, and social sciences. The chosen applications clearly and concisely demonstrate how numerical techniques can be, and often must be, applied in real-life situations.

Content

1. Mathematical Preliminaries and Error Analysis
2. Solutions of Equations in One Variable
3. Interpolation and Polynomial Approximation
4. Numerical Differentiation and Integration
5. Initial-Value Problems for Ordinary Differential Equations
6. Direct Methods for Solving Linear Systems
7. IterativeTechniques in Matrix Algebra
8. ApproximationTheory
9. Approximating Eigenvalues
10. Numerical Solutions of Nonlinear Systems of Equations
11. Boundary-Value Problems for Ordinary Differential Equations
12. Numerical Solutions to Partial Differential Equations

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