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This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.

Fourier transformations. --- Laplace transformation. --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics) --- Transformations, Fourier --- Transforms, Fourier --- Fourier analysis

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Programming --- programmeertalen --- Planning (firm) --- Computer science --- Operational research. Game theory --- Programming (Mathematics) --- Linear programming --- Programmation (Mathématiques) --- Programmation linéaire --- Linear Programming --- Linear programming. --- 519.72 --- Matrices --- Production scheduling --- Substitutions, Linear --- Transformations (Mathematics) --- Vector analysis --- Mathematical programming --- Goal programming --- Algorithms --- Functional equations --- Mathematical optimization --- Operations research --- Programming (Mathematics). --- Programmation (Mathématiques) --- Programmation linéaire

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Consisting of 16 refereed original contributions, this volume presents a diversified collection of recent results in control of distributed parameter systems. Topics addressed include - optimal control in fluid mechanics - numerical methods for optimal control of partial differential equations - modeling and control of shells - level set methods - mesh adaptation for parameter estimation problems - shape optimization Advanced graduate students and researchers will find the book an excellent guide to the forefront of control and estimation of distributed parameter systems.

Wave equation --- Existence theorems --- Multivariate analysis --- Differential equations, Partial --- Dynamics. --- Ergodic theory. --- Dynamical Systems and Ergodic Theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Wave equation - Congresses. --- Existence theorems - Congresses. --- Multivariate analysis - Congresses. --- Differential equations, Partial - Congresses.

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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

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This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations, with tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explainig theory in terms of relevant examples from real systems, this book is user- friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. The new revised and updated edition includes a new chapter on useful effects of fast vibrations and many new exercise problems.

534.8 --- Applications of acoustics (theory) --- Vibration. --- 534.8 Applications of acoustics (theory) --- Vibration --- Cycles --- Mechanics --- Sound --- Mechanical engineering. --- Dynamical systems. --- Dynamics. --- Mechanics. --- Mechanics, Applied. --- Statistical physics. --- Applied mathematics. --- Engineering mathematics. --- Ergodic theory. --- Mechanical Engineering. --- Vibration, Dynamical Systems, Control. --- Solid Mechanics. --- Complex Systems. --- Applications of Mathematics. --- Dynamical Systems and Ergodic Theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Engineering --- Engineering analysis --- Mathematical analysis --- Physics --- Mathematical statistics --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Machinery --- Steam engineering --- Statistical methods