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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis
Analysis in singular spaces is becoming an increasingly important
area of research, with motivation coming from the calculus of
variations, PDEs, geometric analysis, metric geometry and
probability theory, just to mention a few areas. In all these
fields, the role of measure theory is crucial and an appropriate
understanding of the interaction between the relevant
measure-theoretic framework and the objects under investigation is
important to a successful research. The aim of this book, which
gathers contributions from leading specialists with different
backgrounds, is that of creating a collection of various aspects of
measure theory occurring in recent research with the hope of
increasing interactions between different fields. List of
contributors: Luigi Ambrosio, Vladimir I. Bogachev, Fabio
Cavalletti, Guido De Philippis, Shouhei Honda, Tom Leinster,
Christian Leonard, Andrea Marchese, Mark W. Meckes, Filip Rindler,
Nageswari Shanmugalingam, Takashi Shioya, and Christina Sormani.
Using the familiar software Microsoft ® Excel, this book examines
the applications of complex variables. Implementation of the
included problems in Excel eliminates the “black box” nature of
more advanced computer software and programming languages and
therefore the reader has the chance to become more familiar with
the underlying mathematics of the complex variable problems. This
book consists of two parts. In Part I, several topics are covered
that one would expect to find in an introductory text on complex
variables. These topics include an overview of complex numbers,
functions of a complex variable, and the Cauchy integral formula.
In particular, attention is given to the study of analytic complex
variable functions. This attention is warranted because of the
property that the real and imaginary parts of an analytic complex
variable function can be used to solve the Laplace partial
differential equation (PDE). Laplace's equation is ubiquitous
throughout science and engineering as it can be used to model the
steady-state conditions of several important transport processes
including heat transfer, soil-water flow, electrostatics, and ideal
fluid flow, among others. In Part II, a specialty application of
complex variables known as the Complex Variable Boundary Element
Method (CVBEM) is examined. CVBEM is a numerical method used for
solving boundary value problems governed by Laplace's equation.
This part contains a detailed description of the CVBEM and a guide
through each step of constructing two CVBEM programs in Excel. The
writing of these programs is the culminating event of the book.
Students of complex variables and anyone with interest in a novel
method for approximating potential functions using the principles
of complex variables are the intended audience for this book. The
Microsoft Excel applications (including simple programs as well as
the CVBEM program) covered will also be of interest in the
industry, as these programs are accessible to anybody with
Microsoft Office.
Containing selected papers on the fundamentals and applications of
Complexity Science, this multi-disciplinary book presents new
approaches for resolving complex issues that cannot be resolved
using conventional mathematical or software models. Complex Systems
problems can occur in a variety of areas such as physical sciences
and engineering, the economy, the environment, humanities and
social and political sciences. Complexity Science problems, the
science of open systems consisting of large numbers of diverse
components engaged in rich interaction, can occur in a variety of
areas such as physical sciences and engineering, the economy, the
environment, humanities and social and political sciences. The
global behaviour of these systems emerges from the interaction of
constituent components and is unpredictable but not random. The key
attribute of Complex Systems is the ability to self-organise and
adapt to unpredictable changes in their environment. Renown
complexity thinkers and practitioners as well as those who are new
to the area of complexity will find interest in this book.
Nonsmooth Analysis is a relatively recent area of mathematical
analysis. The literature about this subject consists mainly in
research papers and books. The purpose of this book is to provide a
handbook for undergraduate and graduate students of mathematicsthat
introduce this interesting area in detail.
Includes different kinds of sub and super differentials as well as
generalized gradientsIncludes also the main tools of the theory, as
Sum and Chain Rules or Mean Value theoremsContent isintroduced in
an elementary way, developing many examples, allowing the reader to
understand a theory which is scattered in many papers and research
books"
Effective Dynamics of Stochastic Partial Differential Equations
focuses on stochastic partial differential equations with slow and
fast time scales, or large and small spatial scales. The authors
have developed basic techniques, such as averaging, slow manifolds,
and homogenization, to extract effective dynamics from these
stochastic partial differential equations.
The authors experience both as researchers and teachers enable
them to convert current research on extracting effective dynamics
of stochastic partial differential equations into concise and
comprehensive chapters. The book helps readers by providing an
accessible introduction to probability tools in Hilbert space and
basics of stochastic partial differential equations. Each chapter
also includes exercises and problems to enhance
comprehension.
New techniques for extracting effective dynamics of infinite
dimensional dynamical systems under uncertaintyAccessible
introduction to probability tools in Hilbert space and basics of
stochastic partial differential equationsSolutions or hints to all
Exercises"
Offering a concise collection of MatLab programs and exercises to
accompany a third semester course in multivariable calculus, "A
MatLab Companion for Multivariable Calculus" introduces simple
numerical procedures such as numerical differentiation, numerical
integration and Newton's method in several variables, thereby
allowing students to tackle realistic problems. The many examples
show students how to use MatLab effectively and easily in many
contexts. Numerous exercises in mathematics and applications areas
are presented, graded from routine to more demanding projects
requiring some programming. Matlab M-files are provided on the
Harcourt/Academic Press web site at http:
//www.harcourt-ap.com/matlab.html.
* Computer-oriented material that complements the essential topics
in multivariable calculus
* Main ideas presented with examples of computations and graphics
displays using MATLAB
* Numerous examples of short code in the text, which can be
modified for use with the exercises
* MATLAB files are used to implement graphics displays and contain
a collection of mfiles which can serve as demos
Complex Systems occur in an infinite variety of problems, not only
in the realm of physical sciences and engineering, but encompassing
fields as diverse as economy, the environment, humanities, social
and political sciences. The high level of dynamics of such systems,
which is usually expressed through the frequent occurrence of
unpredictable disruptive events, makes conventional optimizers,
batch schedulers and resource planning systems unworkable. Composed
of selected research papers, this book brings together new
developments and processes for managing complexity. The included
works originate from renowned complexity thinkers, well established
practitioners and new researchers in the field and detail issues of
common interest. This title will particularly appeal to
researchers, developers and users of complex systems from a variety
of disciplines, alongside specialists in modelling complex issues.
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.
Precise approach with definitions, theorems, proofs, examples and
exercises. Topics include partial differentiation, vectors,
differential geometry, Stieltjes integral, infinite series, gamma
function, Fourier series, Laplace transform, much more. Numerous
graded exercises with selected answers.
This proceedings volume collects select contributions presented at
the International Conference in Operator Theory held at Hammamet,
Tunisia, on April 30 May 3, 2018. Edited and refereed by well-known
experts in the field, this wide-ranging collection of survey and
research articles presents the state of the art in the field of
operator theory, covering topics such as operator and spectral
theory, fixed point theory, functional analysis etc.
With a long history of innovation in the market, Larson/Edwards'
Calculus, International Metric Edition has been widely praised by a
generation of students and professors for solid and effective
pedagogy that addresses the needs of a broad range of teaching and
learning styles and environments. This edition clearly presents and
effectively demonstrates the concepts and rules of calculus with a
student-focused approach. It offers a wealth of learning support
and digital resources - all thoroughly updated and refined using
proven learning design principles that remove typical barriers to
learning to create a carefully planned, inclusive experience for
all students.
This book serves as a textbook in real analysis. It focuses on the
fundamentals of the structural properties of metric spaces and
analytical properties of functions defined between such spaces.
Topics include sets, functions and cardinality, real numbers,
analysis on R, topology of the real line, metric spaces, continuity
and differentiability, sequences and series, Lebesgue integration,
and Fourier series. It is primarily focused on the applications of
analytical methods to solving partial differential equations rooted
in many important problems in mathematics, physics, engineering,
and related fields. Both the presentation and treatment of topics
are fashioned to meet the expectations of interested readers
working in any branch of science and technology. Senior
undergraduates in mathematics and engineering are the targeted
student readership, and the topical focus with applications to
real-world examples will promote higher-level mathematical
understanding for undergraduates in sciences and engineering.
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