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A First Course on Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopaedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB, with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science and industrial mathematics.
Numerical Algorithms.
Roundoff Errors.
Nonlinear Equations in One Variable.
Linear Algebra Background.
Linear Systems: Direct Methods.
Linear Least Squares Problems.
Linear Systems: Iterative Methods.
Eigenvalues and Singular Values.
Nonlinear Systems and Optimization.
Polynomial Interpolation.
Piecewise Polynomial Interpolation.
Best Approximation.
Fourier Transform.
Numerical Differentiation.
Numerical Integration.
Differential Equations