Titlebook: Scientific Computing with MATLAB and Octave; Alfio Quarteroni,Fausto Saleri Textbook 20062nd edition Springer-Verlag Berlin Heidelberg 200

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Numerical differentiation and integration,In this chapter we propose methods for the numerical approximation of derivatives and integrals of functions. Concerning integration, quite often for a generic function it is not possible to find a primitive in an explicit form. Even when a primitive is known, its use might not be easy.

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Eigenvalues and eigenvectors,Given a square matrix A ∈ℂ., the eigenvalue problem consists in finding a scalar λ (real or complex) and a nonnull vector . such that

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Numerical methods for (initial-)boundary-value problems,Boundary-value problems are differential problems set in an interval (., .) of the real line or in an open multidimensional region Ω ⊂ ℝ. (. = 2, 3) for which the value of the unknown solution (or its derivatives) is prescribed at the end-points . and . of the interval, or on the boundary ∂Ω of the multidimensional region.

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Solutions of the exercises,Solution 1.1 Only the numbers of the form ±0.1. · 2. with . = 0,1 and e = ±2,±1,0 belong to the set F(2, 2,−2, 2). For a given exponent, we can represent in this set only the two numbers 0.10 and 0.11, and their opposites. Consequently, the number of elements belonging to F(2, 2,−2, 2) is 20. Finally, ∈. = ½.

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Alfio Quarteroni,Fausto SaleriEasy introduction to scientific computing.Very suitable for the scientific computing part of the everywhere growing CSE courses.Eminently suitable for physicists, chemists, engineers and other scienti

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