Functional Analysis In Applied Mathematics And Engineering
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| Author | : Michael Pedersen |
| Publisher | : Routledge |
| Total Pages | : 312 |
| Release | : 2018-10-03 |
| Genre | : Mathematics |
| ISBN | : 1351446908 |
Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering. This text/reference discusses: rudimentary topology Banach's fixed point theorem with applications L^p-spaces density theorems for testfunctions infinite dimensional spaces bounded linear operators Fourier series open mapping and closed graph theorems compact and differential operators Hilbert-Schmidt operators Volterra equations Sobolev spaces control theory and variational analysis Hilbert Uniqueness Method boundary element methods Functional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.
| Author | : Eberhard Zeidler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 503 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461208157 |
The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.
| Author | : Anthony N. Michel |
| Publisher | : Courier Corporation |
| Total Pages | : 514 |
| Release | : 1993-01-01 |
| Genre | : Mathematics |
| ISBN | : 048667598X |
"A valuable reference." — American Scientist. Excellent graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Fundamentals, algebraic structures, vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, linear operators, more. A generous number of exercises have been integrated into the text. 1981 edition.
| Author | : J. Tinsley Oden |
| Publisher | : CRC Press |
| Total Pages | : 610 |
| Release | : 2017-12-01 |
| Genre | : Mathematics |
| ISBN | : 149876116X |
Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces. The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory. The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.
| Author | : Fabio Botelho |
| Publisher | : Springer |
| Total Pages | : 584 |
| Release | : 2014-06-12 |
| Genre | : Mathematics |
| ISBN | : 3319060740 |
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
| Author | : Ward Cheney |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 455 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475735596 |
This well-written book contains the analytical tools, concepts, and viewpoints needed for modern applied mathematics. It treats various practical methods for solving problems such as differential equations, boundary value problems, and integral equations. Pragmatic approaches to difficult equations are presented, including the Galerkin method, the method of iteration, Newton’s method, projection techniques, and homotopy methods.
| Author | : George Bachman |
| Publisher | : Courier Corporation |
| Total Pages | : 548 |
| Release | : 2012-09-26 |
| Genre | : Mathematics |
| ISBN | : 0486136558 |
Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. 1966 edition.
| Author | : Paul Sacks |
| Publisher | : Academic Press |
| Total Pages | : 322 |
| Release | : 2017-05-16 |
| Genre | : Mathematics |
| ISBN | : 0128114576 |
Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. - Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas - Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations - Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
| Author | : Milan Miklavčič |
| Publisher | : Allied Publishers |
| Total Pages | : 316 |
| Release | : 1998 |
| Genre | : |
| ISBN | : 9788177648515 |
| Author | : B.D. Reddy |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 472 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 1461205751 |
Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.
