Numerical Analysis
by Richard L. Burden, J. Douglas Faires, Annette M. Burden
10th Edition
Publisher: Cengage Learning
Book Details
| Print ISBN | 9781305253667 |
| eText ISBN | 9798214349633 |
| Publisher | Cengage Learning |
| Publishing Year | 2016 |
| Edition | 10th Edition |
| Language | English |
| Pages | 918 |
In the rapidly evolving landscape of scientific computing and quantitative analysis, mastering mathematical approximation is more critical than ever. Numerical Analysis 10th Edition stands as the definitive guide for students navigating this complex domain, offering a balanced and highly accessible introduction to modern approximation techniques. By bridging the gap between pure mathematical theory and practical computational application, this text helps learners understand not only how algorithms function but also when and why they can be expected to succeed or fail. It remains an indispensable resource for anyone looking to build a solid foundation in computational mathematics, ensuring that students develop the necessary analytical skills to evaluate the validity of their numerical results in real-world scenarios.
The authors construct a rigorous yet intuitive framework that requires only a basic prerequisite of single-variable calculus. Throughout the text, readers explore foundational themes such as error analysis, root-finding algorithms, interpolating polynomials, numerical integration, and the numerical solution of differential equations. By focusing on the conceptual underpinnings of each method, the writing team ensures that students develop a deep, structural intuition for mathematical modeling rather than merely memorizing formulas. This balanced perspective is crucial for tackling modern challenges in engineering, physical sciences, computer science, and quantitative finance, where precise approximations are essential for system design and analysis.
Designed primarily for a one- or two-semester undergraduate course, Numerical Analysis 10th Edition is highly favored by instructors for its wealth of real-world examples and diverse exercise sets. These practical scenarios demonstrate how numerical methods solve everyday problems in computing, aerospace, and physical science disciplines. For students seeking a flexible and portable learning format, acquiring the Numerical Analysis 10th Edition PDF provides seamless access to these vital resources, helping them study complex algorithms on any digital device. This edition continues to set the benchmark for undergraduate mathematical analysis instruction worldwide, preparing the next generation of researchers for advanced quantitative work and computational problem-solving.
Table of Contents
Chapter 1: Mathematical Preliminaries and Error Analysis
- • Review of Calculus
- • Round-off Errors and Computer Arithmetic
- • Algorithms and Convergence
Chapter 2: Solutions of Equations in One Variable
- • The Bisection Method
- • Fixed-Point Iteration
- • Newton's Method and Its Extensions
- • Error Analysis for Iterative Methods
Chapter 3: Interpolation and Polynomial Approximation
- • Interpolation and the Lagrange Polynomial
- • Data Approximation and Neville's Method
- • Divided Differences
- • Hermite Interpolation
- • Cubic Spline Interpolation
Chapter 4: Numerical Differentiation and Integration
- • Numerical Differentiation
- • Richardson's Extrapolation
- • Elements of Numerical Integration
- • Composite Numerical Integration
- • Adaptive Quadrature Methods
- • Romberg Integration
Chapter 5: Initial-Value Problems for Ordinary Differential Equations
- • The Elementary Theory of Initial-Value Problems
- • Euler's Method
- • Higher-Order Taylor Methods
- • Runge-Kutta Methods
- • Error Control and the Runge-Kutta-Fehlberg Method
Chapter 6: Direct Methods for Solving Linear Systems
- • Linear Systems of Equations
- • Pivot Strategies
- • Linear Algebra and Matrix Inversion
- • The Determinant of a Matrix
- • Matrix Factorization
- • Special Types of Matrices
Chapter 7: Iterative Techniques in Matrix Algebra
- • Norms of Vectors and Matrices
- • Eigenvalues and Eigenvectors
- • The Jacobi and Gauss-Siedel Iterative Techniques
- • Relaxation Techniques for Solving Linear Systems
Chapter 8: Approximation Theory
- • Discrete Least-Squares Approximation
- • Orthogonal Polynomials and Least-Squares Approximation
- • Chebyshev Polynomials
- • Rational Function Approximation
- • Trigonometric Polynomial Approximation
Chapter 9: Approximating Eigenvalues
- • Linear Algebra and Eigenvalues
- • The Power Method
- • Householder's Method
- • The QR Algorithm
Chapter 10: Numerical Solutions of Nonlinear Systems of Equations
- • Fixed Points for Functions of Several Variables
- • Newton's Method for Systems
- • Quasi-Newton Methods
- • Homotopy and Continuation Methods
Chapter 11: Boundary-Value Problems for Ordinary Differential Equations
- • The Linear Shooting Method
- • The Linear Finite-Difference Method
- • The Nonlinear Shooting Method
- • Finite-Difference Methods for Nonlinear Problems
Chapter 12: Numerical Solutions to Partial Differential Equations
- • Elliptic Partial Differential Equations
- • Parabolic Partial Differential Equations
- • Hyperbolic Partial Differential Equations
- • An Introduction to the Finite-Element Method
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- Numerical Analysis by: Burden/Faires/Burden - 9798214349633
- [PDF] Numerical Analysis, 9th ed.
- (PDF) Numerical Analysis, 10th ed. - ResearchGate
- Numerical Analysis, 10e Companion Website
- Numerical Analysis, 10e - MATLAB & Simulink Books - MathWorks
- Textbooks - Mathematics and Statistics | SFASU
- Numerical Analysis | Buy | 9781305253667 - eCampus.com
- [PDF] Numerical Analysis, 9th ed.
- Numerical Analysis, 10th Edition [10 ed.] 1305465350, 1305253663 ...
- Numerical Analysis, 10th Edition - 9781305253667 - Cengage UK
- Numerical Analysis, 10th Edition - 9781305253667 - Cengage
- Numerical Analysis - 10th Edition - Solutions and Answers - Quizlet
- Numerical Analysis 10th Edition 10nbsped 1305465350 ... - Scribd
- Numerical Analysis 10th Edition solutions - StudySoup
