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quarteroni scientific computing matlab octave 3ed 2010 rep

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Textbook in PDF format This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material. What can’t be ignored The MATLAB and Octave environments Real numbers Complex numbers Matrices Real functions To err is not only human The MATLAB language What we haven’t told you Exercises Nonlinear equations Some representative problems The bisection method The Newton method The secant method Systems of nonlinear equations Fixed point iterations Acceleration using Aitken method Algebraic polynomials What we haven’t told you Exercises Approximation of functions and data Some representative problems Approximation by Taylor’s polynomials Interpolation Piecewise linear interpolation Approximation by spline functions The least-squares method What we haven’t told you Exercises Numerical differentiation and integration Some representative problems Approximation of function derivatives Numerical integration Interpolatory quadratures Simpson adaptive formula Monte Carlo Methods for Numerical Integration What we haven’t told you Exercises Linear systems Some representative problems Linear system and complexity The LU factorization method The pivoting technique How accurate is the solution of a linear system How to solve a tridiagonal system Overdetermined systems What is hidden behind the MATLAB command Iterative methods Richardson and gradient methods The conjugate gradient method When should an iterative method be stopped To wrap-up direct or iterative What we haven’t told you Exercises Eigenvalues and eigenvectors Some representative problems The power method Generalization of the power method How to compute the shift Computation of all the eigenvalues What we haven’t told you Exercises Ordinary differential equations Some representative problems The Cauchy problem Euler methods The Crank-Nicolson method Zero-stability Stability on unbounded intervals High order methods The predictor-corrector methods Systems of differential equations Some examples What we haven’t told you Exercises Numerical approximation of boundary-value problems Some representative problems Approximation of boundary-value problems Hyperbolic equations a scalar pure advection problem The wave equation What we haven’t told you Exercises Solutions of the exercises

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Quarteroni A. Scientific Computing with MATLAB and Octave 3ed 2010.pdf 4.5 MB
Quarteroni A., Gervasio P. A Primer on Mathematical Modelling 2020.pdf 6.9 MB

Details for: Quarteroni A. Scientific Computing with MATLAB and Octave 3ed 2010 Rep

quarteroni scientific computing matlab octave 3ed 2010 rep