This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.
@bul:* a unique blend of theory and applications
- two brand new chapters on eigenvalues and splines
- inclusion of formal algorithms
- numerous fully worked examples
- a large number of problems, many with solutions
Advanced undergraduate students in math, computer science, engineering and physical sciences
(Chapter Heading): Introduction. Basic Analysis. Taylors Polynomial and Series. The Interpolating Polynomial. Best Approximation. Splines and Other Approximations. Numerical Integration and Differentiation. Solution of Algebraic Equations of One Variable. Linear Equations. Matrix Norms and Applications. Matrix Eigenvalues and Eigenvectors. Systems of Non-linear Equations. Ordinary Differential Equations. Boundary Value and Other Methods for Ordinary Differential Equations. Appendices. Solutions to Selected Problems. References. Subject Index.
Introduction: What is Numerical Analysis? Numerical Algorithms. Properly Posed and Well-Conditioned Problems. Basic Analysis: Functions. Limits and Derivatives. Sequences and Series. Integration. Logarithmic and Exponential Functions. Taylor's Polynomial and Series: Function Approximation. Taylor's Theorem. Convergence of Taylor Series. Taylor Series in Two Variables. Power Series. The Interpolating Polyomial: Linear Interpolation. Polynomial Interpolation. Accuracy of Interpolation. The NevilleAitken Algorithm. Inverse Interpolation. Divided Differences. Equally Spaced Points. Derivatives and Differences. Effect of Rounding Error. Choice of Interpolation Points. Examples of Bernstein and Runge. "Best"Approximation: Norms of Functions. Best Approximations. Least Squares Approximations. Orthogonal Functions. Orthogonal Polynomials. Minimax Approximation. Chebyshev Series. Economization of Power Series. The Remez Algorithms. Further Results on Minimax Approximation.Splines and Other Approximations: Introduction. B-Splines. Equally-Spaced Knots. Hermite Interpolation. Pade and Rational Approximation. Numerical Integration and Differentiation: Numerical Integration. Romberg Integration. Gaussian Integration. Indefinite Integrals. Improper Integrals. Multiple Integrals. Numerical Differe
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- © Academic Press 1996
- 5th July 1996
- Academic Press
- eBook ISBN:
- Paperback ISBN:
George M. Phillips is Reader in Mathematics at the University of St. Andrews, UK. His longstanding collaboration in mathematics has encompassed both teaching and research. Both authors have published many papers in numerical analysis and approximation theory.
University of St. Andrews
Peter J. Taylor is a retired Senior Lecturer from the University of Strathclyde, UK. His longstanding collaboration in mathematics has encompassed both teaching and research. Both authors have published many papers in numerical analysis and approximation theory.
University of Strathclyde, UK
@qu:The first edition was an outstanding work, and the additions that have been put in the Second Edition are very appropriate and have been written up in exemplary fashion. @source:--Philip J. Davis