Analysis and Differential Equations (2版)

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The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations. The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied. Request Inspection Copy Sample Chapter(s) Preface of the second edition Chapter 1: Introduction Contents: Introduction Expansions with Orthogonal Polynomials Differential and Integral Calculus Linear Differential Equations Linear Differential Equations in ℝp Partial Differential Equations Special Functions Solutions Readership: Undergraduate and graduate students in mathematics courses of analysis and differential calculus; researchers in mathematics.

PROBABILITY AND STOCHASTIC PROCESSES: WORK EXAMPLES

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The book is intended to undergraduate students, it presents exercices and problems with rigorous solutions covering the mains subject of the course with both theory and applications. The questions are solved using simple mathematical methods: Laplace and Fourier transforms provide direct proofs of the main convergence results for sequences of random variables. The book studies a large range of distribution functions for random variables and processes: Bernoulli, multinomial, exponential, Gamma, Beta, Dirichlet, Poisson, Gaussian, Chi2, ordered variables, survival distributions and processes, Markov chains and processes, Brownian motion and bridge, diffusions, spatial processes. Sample Chapter(s) Preface Chapter 1: Probability measures and spaces Errata(s) Errata Request Inspection Copy Contents: Probability Measures and Spaces Probability Distributions Generating Function and Discrete Distributions Laplace Transform and Characteristic Function Continuous Distributions Empirical Processes and Weak Convergence Discrete Martingales and Stopping Times Time-Continuous Martingales Jump Processes Continuous Processes Readership: Undergraduate students interested in more advanced statistics.

Agencia ELE Nueva edición 2 (A2) - Libro de ejerciciosl 練習本 (1版)

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【簡介】 Método de español destinado a estudiantes jóvenes y adultos. Nivel A2 MCER.Nueva edición revisada y actualizada de nuestro manual Agencia ELE.Curso comunicativo de español orientado a la acción. El equipo de autores (profesores de institutos Cervantes, EOI y universidades de prestigio) propone una metodología con enfoque orientado a la acción, conforme a las recomendaciones del MCER. El libro de ejercicios es un complemento del libro de clase. Consta de 10 unidades, cada una de las cuales propone una serie de actividades para reforzar los contenidos que ya han aparecido en el libro de clase. Una nueva sección (Algo más) con actividades de refuerzo. Incluye las transcripciones de las audiciones y un solucionario, con la respuesta a los ejercicios, al final del libro.Los audios se pueden descartar en el Aula Electrónica: ele.sgel.es/descargas.asp. Esta nueva edición ofrece vídeos en nuestro canal YouTube. Dispone de licencia digital la edición impresa. En la web: Versión digital en Blinklearning; Unidad de muestra en www.sgel.es/ele; Audio descargable en el Aula Electrónica: ele.sgel.es/descargas.asp; Vídeos (en preparación; Libro del profesor (en preparación). 【目錄】