Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms (Hardcover)

Anne Greenbaum, Timothy P. Chartier

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<內容簡介>

Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results.


The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online.

<章節目錄>

Preface
Ch1: MATHEMATICAL MODELING
Ch 2: BASIC OPERATIONS WITH MATLAB
Ch3: MONTE CARLO METHODS
Ch4: SOLUTION OF A SINGLE NONLINEAR EQUATION IN ONE UNKNOWN
Ch5: FLOATING-POINT ARITHMETIC
Ch6: CONDITIONING OF PROBLEMS; STABILITY OF ALGORITHMS
Ch7: DIRECT METHODS FOR SOLVING LINEAR SYSTEMS AND LEAST SQUARES PROBLEMS
Ch8: POLYNOMIAL AND PIECEWISE POLYNOMIAL INTERPOLATION
Ch9: NUMERICAL DIFFERENTIATION AND RICHARDSON EXTRAPOLATION
Ch10: NUMERICAL INTEGRATION
Ch11: NUMERICAL SOLUTION OF THE INITIAL VALUE PROBLEM FOR ORDINARY DIFFERENTIAL EQUATIONS
Ch12: MORE NUMERICAL LINEAR ALGEBRA: EIGENVALUES AND ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS
Ch13: NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEMS
Ch14: NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
APPENDIX A REVIEW OF LINEAR ALGEBRA
APPENDIX B TAYLOR'S THEOREM IN MULTIDIMENSIONS
References
Index