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This book presents important contributions to modern theories
concerning the distribution theory applied to convex analysis
(convex functions, functions of lower semicontinuity, the
subdifferential of a convex function). The authors prove several
basic results in distribution theory and present ordinary
differential equations and partial differential equations by
providing generalized solutions. In addition, the book deals with
Sobolev spaces, which presents aspects related to variation
problems, such as the Stokes system, the elasticity system and the
plate equation. The authors also include approximate formulations
of variation problems, such as the Galerkin method or the finite
element method. The book is accessible to all scientists, and it is
especially useful for those who use mathematics to solve
engineering and physics problems. The authors have avoided concepts
and results contained in other books in order to keep the book
comprehensive. Furthermore, they do not present concrete simplified
models and pay maximal attention to scientific rigor.
This book highlights the remarkable importance of special
functions, operational calculus, and variational methods. A
considerable portion of the book is dedicated to second-order
partial differential equations, as they offer mathematical models
of various phenomena in physics and engineering. The book provides
students and researchers with essential help on key mathematical
topics, which are applied to a range of practical problems. These
topics were chosen because, after teaching university courses for
many years, the authors have found them to be essential, especially
in the contexts of technology, engineering and economics. Given the
diversity topics included in the book, the presentation of each is
limited to the basic notions and results of the respective
mathematical domain. Chapter 1 is devoted to complex functions.
Here, much emphasis is placed on the theory of holomorphic
functions, which facilitate the understanding of the role that the
theory of functions of a complex variable plays in mathematical
physics, especially in the modeling of plane problems. In addition,
the book demonstrates the importance of the theories of special
functions, operational calculus, and variational calculus. In the
last chapter, the authors discuss the basic elements of one of the
most modern areas of mathematics, namely the theory of optimal
control.
This book presents, in a uniform way, several problems in applied
mechanics, which are analysed using the matrix theory and the
properties of eigenvalues and eigenvectors. It reveals that various
problems and studies in mechanical engineering produce certain
patterns that can be treated in a similar way. Accordingly, the
same mathematical apparatus allows us to study not only
mathematical structures such as quadratic forms, but also mechanics
problems such as multibody rigid mechanics, continuum mechanics,
vibrations, elastic and dynamic stability, and dynamic systems. In
addition, the book explores a wealth of engineering applications.
This book offers engineering students an introduction to the theory
of partial differential equations and then guiding them through the
modern problems in this subject. Divided into two parts, in the
first part readers already well-acquainted with problems from the
theory of differential and integral equations gain insights into
the classical notions and problems, including differential
operators, characteristic surfaces, Levi functions, Green's
function, and Green's formulas. Readers are also instructed in the
extended potential theory in its three forms: the volume potential,
the surface single-layer potential and the surface double-layer
potential. Furthermore, the book presents the main initial boundary
value problems associated with elliptic, parabolic and hyperbolic
equations. The second part of the book, which is addressed first
and foremost to those who are already acquainted with the notions
and the results from the first part, introduces readers to modern
aspects of the theory of partial differential equations.
This book highlights the remarkable importance of special
functions, operational calculus, and variational methods. A
considerable portion of the book is dedicated to second-order
partial differential equations, as they offer mathematical models
of various phenomena in physics and engineering. The book provides
students and researchers with essential help on key mathematical
topics, which are applied to a range of practical problems. These
topics were chosen because, after teaching university courses for
many years, the authors have found them to be essential, especially
in the contexts of technology, engineering and economics. Given the
diversity topics included in the book, the presentation of each is
limited to the basic notions and results of the respective
mathematical domain. Chapter 1 is devoted to complex functions.
Here, much emphasis is placed on the theory of holomorphic
functions, which facilitate the understanding of the role that the
theory of functions of a complex variable plays in mathematical
physics, especially in the modeling of plane problems. In addition,
the book demonstrates the importance of the theories of special
functions, operational calculus, and variational calculus. In the
last chapter, the authors discuss the basic elements of one of the
most modern areas of mathematics, namely the theory of optimal
control.
This book presents, in a uniform way, several problems in applied
mechanics, which are analysed using the matrix theory and the
properties of eigenvalues and eigenvectors. It reveals that various
problems and studies in mechanical engineering produce certain
patterns that can be treated in a similar way. Accordingly, the
same mathematical apparatus allows us to study not only
mathematical structures such as quadratic forms, but also mechanics
problems such as multibody rigid mechanics, continuum mechanics,
vibrations, elastic and dynamic stability, and dynamic systems. In
addition, the book explores a wealth of engineering applications.
This book offers engineering students an introduction to the theory
of partial differential equations and then guiding them through the
modern problems in this subject. Divided into two parts, in the
first part readers already well-acquainted with problems from the
theory of differential and integral equations gain insights into
the classical notions and problems, including differential
operators, characteristic surfaces, Levi functions, Green's
function, and Green's formulas. Readers are also instructed in the
extended potential theory in its three forms: the volume potential,
the surface single-layer potential and the surface double-layer
potential. Furthermore, the book presents the main initial boundary
value problems associated with elliptic, parabolic and hyperbolic
equations. The second part of the book, which is addressed first
and foremost to those who are already acquainted with the notions
and the results from the first part, introduces readers to modern
aspects of the theory of partial differential equations.
This book presents important contributions to modern theories
concerning the distribution theory applied to convex analysis
(convex functions, functions of lower semicontinuity, the
subdifferential of a convex function). The authors prove several
basic results in distribution theory and present ordinary
differential equations and partial differential equations by
providing generalized solutions. In addition, the book deals with
Sobolev spaces, which presents aspects related to variation
problems, such as the Stokes system, the elasticity system and the
plate equation. The authors also include approximate formulations
of variation problems, such as the Galerkin method or the finite
element method. The book is accessible to all scientists, and it is
especially useful for those who use mathematics to solve
engineering and physics problems. The authors have avoided concepts
and results contained in other books in order to keep the book
comprehensive. Furthermore, they do not present concrete simplified
models and pay maximal attention to scientific rigor.
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