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Numerical Analysis


ISBN13: 9780691146867|342 pages|Hardcover|©2011|
L. Ridgway Scott

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks.
Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases.
The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject.
-Presents the mathematical foundations of numerical analysis
-Explains the mathematical details behind simulation software
-Introduces many advanced concepts in modern analysis
-Self-contained and mathematically rigorous
-Contains problems and solutions in each chapter
-Excellent follow-up course to Principles of Mathematical Analysis by Rudin

Table of Contents
Chapter 1. Numerical Algorithms 1
Chapter 2. Nonlinear Equations 15
Chapter 3. Linear Systems 35
Chapter 4. Direct Solvers 51
Chapter 5. Vector Spaces 65
Chapter 6. Operators 81
Chapter 7. Nonlinear Systems 97
Chapter 8. Iterative Methods 115
Chapter 9. Conjugate Gradients 133
Chapter 10. Polynomial Interpolation 151
Chapter 11. Chebyshev and Hermite Interpolation 167
Chapter 12. Approximation Theory 183
Chapter 13. Numerical Quadrature 203
Chapter 14. Eigenvalue Problems 225
Chapter 15. Eigenvalue Algorithms 241
Chapter 16. Ordinary Differential Equations 257
Chapter 17. Higher-order ODE Discretization Methods 275
Chapter 18. Floating Point 293
Chapter 19. Notation 309