659,99 zł

Functional Differential Equations

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419,99 zł

Techniques Of Functional Analysis For Differential And Integral Equations

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99,76 zł

Applied Functional Analysis Dover Publications Inc.

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PrefacePart I. Distribution Theory and Green's Functions Chapter 1. Generalised Functions 1.1 The Delta function 1.2 Basic distribution theory 1.3 Operations on distributions 1.4 Convergence of distributions 1.5 Further developments 1.6 Fourier Series and the Poisson Sum formula 1.7 Summary and References Problems Chapter 2. Differential Equations and Green's Functions 2.1 The Integral of a distribution 2.2 Linear differential equations 2.3 Fundamental solutions of differential equations 2.4 Green's functions 2.5 Applications of Green's functions 2.6 Summary and References Problems Chapter 3. Fourier Transforms and Partial differential Equations 3.1 The classical Fourier transform 3.2 Distributions of slow growth 3.3 Generalised Fourier transforms 3.4 Generalised functions of several variables 3.5 Green's function for the Laplacian 3.6 Green's function for the Three-dimensional wave equation 3.7 Summary and References ProblemsPart II. Banach spaces and fixed point theorems Chapter 4. Normed spaces 4.1 Vector spaces 4.2 Normed spaces 4.3 Convergence 4.4 Open and closed sets 4.5 Completeness 4.6 Equivalent norms 4.7 Summary and References Problems Chapter 5. The contraction mapping theorem 5.1 Operators on Vector spaces 5.2 The contraction mapping theorem 5.3 Application to differential and integral equations 5.4 Nonlinear diffusive equilibrium 5.5 Nonlinear diffusive equilibrium in three dimensions 5.6 Summary and References Problems Chapter 6. Compactness and Schauder's theorem 6.1 Continuous operators 6.2 Brouwer's theorem 6.3 Compactness 6.4 Relative compactness 6.5 Arzel

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230,53 zł

Introduction to Functional Analysis Birkhauser

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Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.

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299,99 zł

An Introduction To Nonlinear Functional Analysis And Elliptic Problems

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453,96 zł

Numerical Mathematics Springer, Berlin

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Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions.§As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis.§One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems.§This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.§In this second edition, the readability of pictures, tables and program headings have been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added.

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549,39 zł

Fourier Analysis Princeton University Press

Książki / Literatura obcojęzyczna

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences - that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis.Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. "The Princeton Lectures in Analysis" represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which "Fourier Analysis" is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing "Fourier" series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

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739,99 zł

Green's Functions With Applications

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t1=0.019, t2=0, t3=0, t4=0.012, t=0.019