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Differential equations. --- Numerical analysis. --- 517.91 Differential equations --- Differential equations --- Mathematical analysis --- Equacions diferencials --- Anàlisi numèrica --- Mètodes numèrics --- Algorismes --- Anàlisi matemàtica --- Teoria de l'aproximació --- Anàlisi d'error (Matemàtica) --- Anàlisi d'intervals (Matemàtica) --- Càlculs numèrics --- Equacions diferencials estocàstiques --- Integració numèrica --- Interpolació (Matemàtica) --- Mètodes de Galerkin --- Mètode de Montecarlo --- Mètode dels elements finits --- Mètodes iteratius (Matemàtica) --- Nomografia (Matemàtica) --- Rutes aleatòries (Matemàtica) --- Solucions numèriques --- Càlcul --- Funcions de Bessel --- Àlgebra diferencial --- Càlcul integral --- Càlcul operacional --- Equacions d'evolució --- Equacions de camp d'Einstein --- Equacions de Lagrange --- Equacions de Pfaff --- Equacions diferencials algebraiques --- Equacions diferencials ordinàries --- Equacions en derivades parcials --- Funcions de Green --- Funcions de Lyapunov --- Problemes de contorn --- Problemes inversos (Equacions diferencials) --- Teoria d'estabilitat (Matemàtica) --- Transformació de Laplace

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This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice. The text addresses numerical analysis as a middle ground between practice and theory, addressing both the abstract mathematical analysis and applied computation and programming models instrumental to the field. While the text uses pseudocode, Matlab and Julia codes are available online for students to use, and to demonstrate implementation techniques. The textbook also emphasizes multivariate problems alongside single-variable problems and deals with topics in randomness, including stochastic differential equations and randomized algorithms, and topics in optimization and approximation relevant to machine learning. Ultimately, it seeks to clarify issues in numerical analysis in the context of applications, and presenting accessible methods to students in mathematics and data science. .

Differential equations --- Numerical analysis --- differentiaalvergelijkingen --- numerieke analyse

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Most of numerical analysis relies on algorithms for perfoming calculations on matrices and vectors. The operations most needed are ones which solve systems of linear equations, numerically computing the maximum or minimum of a function, or solving differential equations. The Meschach library contains routines to address all of the basic operations for dealing with matrices and vectors, and a number of other issues as well.

Matrix analytic methods.

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In July 1998 the first NEMACOM (NEw Methods in Applied and COmputational Mathematics) workshop was held at the campus of the University of Southern Queensland at Hervey Bay on the Wide-Bay-Burnett coast of Queensland. At the workshop a number of different topics in applied and computational mathematics were presented ranging from computational statistics and stochastic processes, through optimization, optimal control, graph theoretic methods in computational mathematics, the use of dynamical systems techniques for meteorology, modelling the solar atmosphere and geo-hydrological processes, simulating rigid-body dynamics, and the future of the Fast Fourier Transform.

Mathematical analysis

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In July 1998 the first NEMACOM (NEw Methods in Applied and COmputational Mathematics) workshop was held at the campus of the University of Southern Queensland at Hervey Bay on the Wide-Bay-Burnett coast of Queensland. At the workshop a number of different topics in applied and computational mathematics were presented ranging from computational statistics and stochastic processes, through optimization, optimal control, graph theoretic methods in computational mathematics, the use of dynamical systems techniques for meteorology, modelling the solar atmosphere and geo-hydrological processes, simulating rigid-body dynamics, and the future of the Fast Fourier Transform.

Mathematical analysis