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Functional equations. --- Functions of complex variables. --- Series. --- Summability theory.

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Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory. This broad coverage, the authors' clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their studies.

Differential equations --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.91 Differential equations --- 517.91. --- Numerical solutions --- Differential equations. --- 517.91

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Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models ar often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretization is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDE from a Lagrangian point of view and the coupling of particle models. The coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

Differential equations, Partial --- Meshfree methods (Numerical analysis). --- Numerical solutions. --- -Meshfree methods (Numerical analysis) --- Gridless methods (Numerical analysis) --- Meshfree discretization techniques (Numerical analysis) --- Meshless methods (Numerical analysis) --- Meshfree methods (Numerical analysis) --- Numerical analysis --- Numerical solutions --- Conferences - Meetings --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Difference equations. --- Functional equations. --- Computer mathematics. --- Applied mathematics. --- Engineering mathematics. --- Analysis. --- Partial Differential Equations. --- Difference and Functional Equations. --- Computational Mathematics and Numerical Analysis. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Computer mathematics --- Electronic data processing --- Mathematics --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Partial differential equations --- 517.1 Mathematical analysis --- Analyse numérique. --- Analyse numérique --- Numerical analysis. --- Equations aux derivees partielles --- Methodes numeriques

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"Operator Functions and Localization of Spectra" is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra. In particular bounds for the spectra of integral, differential and integro-differential operators, as well as finite and infinite matrices are established. The volume also presents a systematic exposition of estimates for norms of operator-valued functions and their applications.

Linear operators. --- Operator theory. --- Resolvents (Mathematics) --- Perturbation (Mathematics) --- Spectral theory (Mathematics) --- Linear operators --- Operator theory --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Matrix theory. --- Algebra. --- Functions of complex variables. --- Integral equations. --- Operator Theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Functions of a Complex Variable. --- Integral Equations. --- Equations, Integral --- Functional equations --- Functional analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Mathematical analysis

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All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-c

Holomorphic functions. --- Functional analysis. --- Convexity spaces. --- Convex surfaces. --- Complexes. --- Linear complexes --- Algebras, Linear --- Coordinates --- Geometry --- Line geometry --- Transformations (Mathematics) --- Convex areas --- Convex domains --- Surfaces --- Spaces, Convexity --- Convex sets --- Vector spaces --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functions, Holomorphic --- Functions of several complex variables