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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
Straightforward and easy to read, DIFFERENTIAL EQUATIONS WITH
BOUNDARY-VALUE PROBLEMS, 9E, INTERNATIONAL METRIC EDITION gives you
a thorough overview of the topics typically taught in a first
course in Differential Equations as well as an introduction to
boundary-value problems and partial Differential Equations. Your
study will be supported by a bounty of pedagogical aids, including
an abundance of examples, explanations, "Remarks" boxes,
definitions, and more.
DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 8E,
International Edition strikes a balance between the analytical,
qualitative, and quantitative approaches to the study of
differential equations. This proven and accessible book speaks to
beginning engineering and math students through a wealth of
pedagogical aids, including an abundance of examples, explanations,
"Remarks" boxes, definitions, and group projects. Written in a
straightforward, readable, and helpful style, the book provides a
thorough treatment of boundary-value problems and partial
differential equations.
DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 8E,
INTERNATIONAL METRIC EDITION strikes a balance between the
analytical, qualitative, and quantitative approaches to the study
of differential equations. Beginning engineering and math students
like you benefit from this accessible text's wealth of pedagogical
aids, including an abundance of examples, explanations, "Remarks"
boxes, definitions, and group projects. Written in a
straightforward, readable, and helpful style, the book provides you
with a thorough treatment of boundary-value problems and partial
differential equations.
Quite a number of phenomena in science and technology, industrial
and/or agricultural production and transport, medical and/or
biological flows and movements, social and/or economical
developments, etc., depend on many variables, and are very much
complicated. Although the detailed knowledge is accumulated in
respective fields, it is meaningful to model and analyze the
essential part of the phenomena in terms of smaller number of
variables, which falls into partial differential equations. This
book aims at providing students and researchers the basic ideas and
the methods to solve problems in various fields. Particular
attention is paid to bridge the gap between mathematics and the
real world. To do this, we start from a simple system with
intuitively understandable physical background, extract the
essential part, formulate into mathematical tools, and then
generalize for further application. Here logical thinking in depth
and wide linking to various fields are sought to construct
intellectual network.
There is an extensive literature in the form of papers (but no
books) on lattice dynamical systems. The book focuses on
dissipative lattice dynamical systems and their attractors of
various forms such as autonomous, nonautonomous and random. The
existence of such attractors is established by showing that the
corresponding dynamical system has an appropriate kind of absorbing
set and is asymptotically compact in some way.There is now a very
large literature on lattice dynamical systems, especially on
attractors of all kinds in such systems. We cannot hope to do
justice to all of them here. Instead, we have focused on key areas
of representative types of lattice systems and various types of
attractors. Our selection is biased by our own interests, in
particular to those dealing with biological applications. One of
the important results is the approximation of Heaviside switching
functions in LDS by sigmoidal functions.Nevertheless, we believe
that this book will provide the reader with a solid introduction to
the field, its main results and the methods that are used to obtain
them.
Hoermander operators are a class of linear second order partial
differential operators with nonnegative characteristic form and
smooth coefficients, which are usually degenerate
elliptic-parabolic, but nevertheless hypoelliptic, that is highly
regularizing. The study of these operators began with the 1967
fundamental paper by Lars Hoermander and is intimately connected to
the geometry of vector fields.Motivations for the study of
Hoermander operators come for instance from
Kolmogorov-Fokker-Planck equations arising from modeling physical
systems governed by stochastic equations and the geometric theory
of several complex variables. The aim of this book is to give a
systematic exposition of a relevant part of the theory of
Hoermander operators and vector fields, together with the necessary
background and prerequisites.The book is intended for self-study,
or as a reference book, and can be useful to both younger and
senior researchers, already working in this area or aiming to
approach it.
The Qualitative Theory of Ordinary Differential Equations (ODEs)
occupies a rather special position both in Applied and Theoretical
Mathematics. On the one hand, it is a continuation of the standard
course on ODEs. On the other hand, it is an introduction to
Dynamical Systems, one of the main mathematical disciplines in
recent decades. Moreover, it turns out to be very useful for
graduates when they encounter differential equations in their work;
usually those equations are very complicated and cannot be solved
by standard methods.The main idea of the qualitative analysis of
differential equations is to be able to say something about the
behavior of solutions of the equations, without solving them
explicitly. Therefore, in the first place such properties like the
stability of solutions stand out. It is the stability with respect
to changes in the initial conditions of the problem. Note that,
even with the numerical approach to differential equations, all
calculations are subject to a certain inevitable error. Therefore,
it is desirable that the asymptotic behavior of the solutions is
insensitive to perturbations of the initial state.Each chapter
contains a series of problems (with varying degrees of difficulty)
and a self-respecting student should solve them. This book is based
on Raul Murillo's translation of Henryk Zoladek's lecture notes,
which were in Polish and edited in the portal Matematyka Stosowana
(Applied Mathematics) in the University of Warsaw.
Extremum Seeking through Delays and PDEs, the first book on the
topic, expands the scope of applicability of the extremum seeking
method, from static and finite-dimensional systems to
infinite-dimensional systems. Readers will find: Numerous
algorithms for model-free real-time optimization are developed and
their convergence guaranteed. Extensions from single-player
optimization to noncooperative games, under delays and pdes, are
provided. The delays and pdes are compensated in the control
designs using the pde backstepping approach, and stability is
ensured using infinite-dimensional versions of averaging theory.
Accessible and powerful tools for analysis. This book is intended
for control engineers in all disciplines (electrical, mechanical,
aerospace, chemical), mathematicians, physicists, biologists, and
economists. It is appropriate for graduate students, researchers,
and industrial users.
This work is devoted to fixed point theory as well as the theory of
accretive operators in Banach spaces. The goal is to develop, in
self-contained way, the main results in both theories. Special
emphasis is given to the study how both theories can be used to
study the existence and uniqueness of solution of several types of
partial differential equations and integral equations.
Study smarter and stay on top of your differential equations course
with the bestselling Schaum's Outline-now with the NEW Schaum's app
and website! Schaum's Outline of Differential Equations, Fifth
Edition is the go-to study guide for all students of science who
need to learn or refresh their knowledge of differential equations.
With an outline format that facilitates quick and easy review and
mirrors the course in scope and sequence, this book helps you
understand basic concepts and get the extra practice you need to
excel in the course. It supports the all major differential
equations textbooks and is useful for study in Calculus (I, II, and
III), Mathematical Modeling, Introductory Differential Equations
and Differential Equations. Chapters include an Introduction to
Modeling and Qualitative Methods, Classifications of First-Order
Differential Equations, Linear Differential Equations, Variation of
Parameters, Initial-Value Problems for Linear Differential
Equations, Graphical and Numerical Methods for Solving First-Order
Differential Equations, Solutions of Linear Differential Equations
with Constant Coefficients by Laplace Transforms, and more.
Features: NEW to this edition: the new Schaum's app and website!
NEW CHAPTERS include Autonomous Differential Equations and
Qualitative Methods; Eigenvalues and Eigenvectors; three chapters
dealing with Solutions of Systems of Autonomous Equations via
Eigenvalues and Eigenvectors (real and distinct, real and equal,
and complex conjugate Eigenvalues) 20 problem-solving videos online
563 solved problems Outline format provides a quick and easy review
of differential equations Clear, concise explanations of
differential equations concepts Hundreds of examples with
explanations of key concepts Supports all major textbooks for
differential equations courses Appropriate for the following
courses: Calculus (I, II, and III), Mathematical Modeling,
Introductory Differential Equations, and Differential Equations
Containing the proceedings from the 41st conference on Boundary
Elements and other Mesh Reduction Methods (BEM/MRM), this book is a
collection of high quality papers that report on advances in
techniques that reduce or eliminate the type of meshes associated
with such methods as finite elements or finite differences. As
design, analysis and manufacture become more integrated the chances
are that the users will be less aware of the capabilities of the
analytical techniques that are at the core of the process. This
reinforces the need to retain expertise in certain specialised
areas of numerical methods, such as BEM/MRM, to ensure that all new
tools perform satisfactorily in the integrated process. The
maturity of BEM since 1978 has resulted in a substantial number of
industrial applications that demonstrate the accuracy, robustness
and easy use of the technique. Their range still needs to be
widened, taking into account the potentialities of the Mesh
Reduction techniques in general. The papers in this volume help to
expand the range of applications as well as the type of materials
in response to industrial and professional requirements.
The introduction of cross diffusivity opens many questions in the
theory of reactiondiffusion systems. This book will be the first to
investigate such problems presenting new findings for researchers
interested in studying parabolic and elliptic systems where
classical methods are not applicable. In addition, The
Gagliardo-Nirenberg inequality involving BMO norms is improved and
new techniques are covered that will be of interest. This book also
provides many open problems suitable for interested Ph.D students.
For courses in Differential Equations and Linear Algebra. The right
balance between concepts, visualisation, applications, and skills
Differential Equations and Linear Algebra provides the conceptual
development and geometric visualisation of a modern differential
equations and linear algebra course that is essential to science
and engineering students. It balances traditional manual methods
with the new, computer-based methods that illuminate qualitative
phenomena - a comprehensive approach that makes accessible a wider
range of more realistic applications. The book combines core topics
in elementary differential equations with concepts and methods of
elementary linear algebra. It starts and ends with discussions of
mathematical modeling of real-world phenomena, evident in figures,
examples, problems, and applications throughout.
This graduate-level introduction to ordinary differential equations
combines both qualitative and numerical analysis of solutions, in
line with Poincare's vision for the field over a century ago.
Taking into account the remarkable development of dynamical systems
since then, the authors present the core topics that every young
mathematician of our time--pure and applied alike--ought to learn.
The book features a dynamical perspective that drives the
motivating questions, the style of exposition, and the arguments
and proof techniques. The text is organized in six cycles. The
first cycle deals with the foundational questions of existence and
uniqueness of solutions. The second introduces the basic tools,
both theoretical and practical, for treating concrete problems. The
third cycle presents autonomous and non-autonomous linear theory.
Lyapunov stability theory forms the fourth cycle. The fifth one
deals with the local theory, including the Grobman-Hartman theorem
and the stable manifold theorem. The last cycle discusses global
issues in the broader setting of differential equations on
manifolds, culminating in the Poincare-Hopf index theorem. The book
is appropriate for use in a course or for self-study. The reader is
assumed to have a basic knowledge of general topology, linear
algebra, and analysis at the undergraduate level. Each chapter ends
with a computational experiment, a diverse list of exercises, and
detailed historical, biographical, and bibliographic notes seeking
to help the reader form a clearer view of how the ideas in this
field unfolded over time.
Quite a number of phenomena in science and technology, industrial
and/or agricultural production and transport, medical and/or
biological flows and movements, social and/or economical
developments, etc., depend on many variables, and are very much
complicated. Although the detailed knowledge is accumulated in
respective fields, it is meaningful to model and analyze the
essential part of the phenomena in terms of smaller number of
variables, which falls into partial differential equations. This
book aims at providing students and researchers the basic ideas and
the methods to solve problems in various fields. Particular
attention is paid to bridge the gap between mathematics and the
real world. To do this, we start from a simple system with
intuitively understandable physical background, extract the
essential part, formulate into mathematical tools, and then
generalize for further application. Here logical thinking in depth
and wide linking to various fields are sought to construct
intellectual network.
This book highlights new developments in the wide and growing field
of partial differential equations (PDE)-constrained optimization.
Optimization problems where the dynamics evolve according to a
system of PDEs arise in science, engineering, and economic
applications and they can take the form of inverse problems,
optimal control problems or optimal design problems. This book
covers new theoretical, computational as well as implementation
aspects for PDE-constrained optimization problems under
uncertainty, in shape optimization, and in feedback control, and it
illustrates the new developments on representative problems from a
variety of applications.
Elementary Number Theory, 6th Edition, blends classical theory with
modern applications and is notable for its outstanding exercise
sets. A full range of exercises, from basic to challenging, helps
students explore key concepts and push their understanding to new
heights. Computational exercises and computer projects are also
available. Reflecting many years of professor feedback, this
edition offers new examples, exercises, and applications, while
incorporating advancements and discoveries in number theory made in
the past few years.
Lectures on Differential Equations provides a clear and concise
presentation of differential equations for undergraduates and
beginning graduate students. There is more than enough material
here for a year-long course. In fact, the text developed from the
author's notes for three courses: the undergraduate introduction to
ordinary differential equations, the undergraduate course in
Fourier analysis and partial differential equations, and a first
graduate course in differential equations. The first four chapters
cover the classical syllabus for the undergraduate ODE course
leavened by a modern awareness of computing and qualitative
methods. The next two chapters contain a well-developed exposition
of linear and nonlinear systems with a similarly fresh approach.
The final two chapters cover boundary value problems, Fourier
analysis, and the elementary theory of PDEs. The author makes a
concerted effort to use plain language and to always start from a
simple example or application. The presentation should appeal to,
and be readable by, students, especially students in engineering
and science. Without being excessively theoretical, the book does
address a number of unusual topics: Massera's theorem, Lyapunov's
inequality, the isoperimetric inequality, numerical solutions of
nonlinear boundary value problems, and more. There are also some
new approaches to standard topics including a rethought
presentation of series solutions and a nonstandard, but more
intuitive, proof of the existence and uniqueness theorem. The
collection of problems is especially rich and contains many very
challenging exercises. Philip Korman is professor of mathematics at
the University of Cincinnati. He is the author of over one hundred
research articles in differential equations and the monograph
Global Solution Curves for Semilinear Elliptic Equations. Korman
has served on the editorial boards of Communications on Applied
Nonlinear Analysis, Electronic Journal of Differential Equations,
SIAM Review, and Differential Equations and Applications.
This monograph contains papers that were delivered at the special
session on Geometric Potential Analysis, that was part of the
Mathematical Congress of the Americas 2021, virtually held in
Buenos Aires. The papers, that were contributed by renowned
specialists worldwide, cover important aspects of current research
in geometrical potential analysis and its applications to partial
differential equations and mathematical physics.
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