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Introduction to Numerical Analysis and Scientific Computing

Langue : Anglais

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Couverture de l’ouvrage Introduction to Numerical Analysis and Scientific Computing

Designed for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number representations, particularly those pertaining to IEEE simple and double-precision standards as used in scientific computer environments such as MATLAB® version 7.

Drawing on their years of teaching students in mathematics, engineering, and the sciences, the authors discuss computer arithmetic as a source for generating round-off errors and how to avoid the use of algebraic expression that may lead to loss of significant figures. They cover nonlinear equations, linear algebra concepts, the Lagrange interpolation theorem, numerical differentiation and integration, and ODEs. They also focus on the implementation of the algorithms using MATLAB®.

Each chapter ends with a large number of exercises, with answers to odd-numbered exercises provided at the end of the book. Throughout the seven chapters, several computer projects are proposed. These test the students' understanding of both the mathematics of numerical methods and the art of computer programming.

Computer Number Systems and Floating Point Arithmetic. Finding Roots of Real Single-Valued Functions. Solving Systems of Linear Equations by Gaussian Elimination. Polynomial Interpolation and Splines Fitting. Numerical Differentiation and Integration. Advanced Numerical Integration. Numerical Solutions of Ordinary Differential Equations (ODEs). Bibliography. Index.

<p>Nabil Nassif received a Diplôme-Ingénieur from the Ecole Centrale de Paris and earned a master's degree in applied mathematics from Harvard University, followed by a PhD under the supervision of Professor Garrett Birkhoff. Since his graduation, Dr. Nassif has been affiliated with the Mathematics Department at the American University of Beirut, where he teaches and conducts research in the areas of mathematical modeling, numerical analysis and scientific computing. Professor Nassif has authored or co-authored about 50 publications in refereed journals and directed 12 PhD theses with an equal number of master's theses. During his career, Professor Nassif has also held several regular and visiting teaching positions in France, Switzerland, U.S.A. and Sweden.</p><p>Dolly Khoueiri Fayyad received her BSc and master's degrees from the American University of Beirut and her PhD degree from the University of Reims in France under the supervision of Professor Nabil Nassif. After earning her doctorate degree and before becoming a faculty member in the Mathematics Department of the American University of Beirut, she taught at the University of Louvain-la-Neuve in Belgium and then in the Sciences Faculty of Lebanon National University. Simultaneously, Dr. Fayyad has conducted research on the numerical solution of time-dependent partial differential equations and more particularly on semi-linear parabolic equations. She has also supervised several master's theses in her research areas.</p>