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Books > Science & Mathematics > Mathematics
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The Mechanic's Companion, or, The Elements and Practice of Carpentry, Joinery, Bricklaying, Masonry, Slating, Plastering, Painting, Smithing and Turning
- Comprehending the Latest Improvements and Containing a Full Description of the Tools Belonging To...
(Hardcover)
Peter 1765-1844 Nicholson
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What do economic chaos and uncertainties mean in rational or
irrational economic theories? How do simple deterministic
interactions among a few variables lead to unpredictable complex
phenomena? Why is complexity of economies causing so many conflicts
and confusions worldwide?This book provides a comprehensive
introduction to recent developments of complexity theory in
economics. It presents different models based on well-accepted
economic mechanisms such as the Solow model, Ramsey model, and
Lucas model. It is focused on presenting complex behaviors, such as
business cycles, aperiodic motion, bifurcations, catastrophes,
chaos, and hidden attractors, in basic economic models with
nonlinear behavior. It shows how complex nonlinear phenomena are
identified from various economic mechanisms and theories. These
models demonstrate that the traditional or dominant economic views
on evolution of, for instance, capitalism market, free competition,
or Keynesian economics, are not generally valid. Markets are
unpredictable and nobody knows with certainty the consequences of
policies or other external factors in economic systems with simple
interactions.
This book presents a collection of problems and solutions in
functional analysis with applications to quantum mechanics.
Emphasis is given to Banach spaces, Hilbert spaces and generalized
functions.The material of this volume is self-contained, whereby
each chapter comprises an introduction with the relevant notations,
definitions, and theorems. The approach in this volume is to
provide students with instructive problems along with
problem-solving strategies. Programming problems with solutions are
also included.
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.
The scientific field of data analysis is constantly expanding due
to the rapid growth of the computer industry and the wide
applicability of computational and algorithmic techniques, in
conjunction with new advances in statistical, stochastic and
analytic tools. There is a constant need for new, high-quality
publications to cover the recent advances in all fields of science
and engineering. This book is a collective work by a number of
leading scientists, computer experts, analysts, engineers,
mathematicians, probabilists and statisticians who have been
working at the forefront of data analysis and related applications.
The chapters of this collaborative work represent a cross-section
of current concerns, developments and research interests in the
above scientific areas. The collected material has been divided
into appropriate sections to provide the reader with both
theoretical and applied information on data analysis methods,
models and techniques, along with related applications.
Fuzzy logic, which is based on the concept of fuzzy set, has
enabled scientists to create models under conditions of
imprecision, vagueness, or both at once. As a result, it has now
found many important applications in almost all sectors of human
activity, becoming a complementary feature and supporter of
probability theory, which is suitable for modelling situations of
uncertainty derived from randomness. Fuzzy mathematics has also
significantly developed at the theoretical level, providing
important insights into branches of traditional mathematics like
algebra, analysis, geometry, topology, and more. With such
widespread applications, fuzzy sets and logic are an important area
of focus in mathematics. Advances and Applications of Fuzzy Sets
and Logic studies recent theoretical advances of fuzzy sets and
numbers, fuzzy systems, fuzzy logic and their generalizations,
extensions, and more. This book also explores the applications of
fuzzy sets and logic applied to science, technology, and everyday
life to further provide research on the subject. This book is ideal
for mathematicians, physicists, computer specialists, engineers,
practitioners, researchers, academicians, and students who are
looking to learn more about fuzzy sets, fuzzy logic, and their
applications.
This resource has been developed to fully cover unit A2 2: Applied
Mathematics of the CCEA specification, addressing both mechanics
and statistics. For each topic, the book begins with a logical
explanation of the theory, examples to reinforce the explanation,
and any key words and definitions that are required. Examples and
definitions are clearly differentiated to ease revision and
progression through the book. The material then flows into
exercises, before introducing the next topic. In this way, the
student is guided through the subject. The book contains a large
number of exercises in order to provide teachers with as much
flexibility as possible for their students. Answers to the
questions are included at the back of the book. Contents: 1
Kinematics; 2 Projectiles; 3 Moments; 4 Impulse and Momentum; 5
Probability; 6 Statistical Distributions; 7 Statistical Hypothesis
Testing
This book is intended as a textbook for a one-term senior
undergraduate (or graduate) course in Ring and Field Theory, or
Galois theory. The book is ready for an instructor to pick up to
teach without making any preparations.The book is written in a way
that is easy to understand, simple and concise with simple historic
remarks to show the beauty of algebraic results and algebraic
methods. The book contains 240 carefully selected exercise
questions of varying difficulty which will allow students to
practice their own computational and proof-writing skills. Sample
solutions to some exercise questions are provided, from which
students can learn to approach and write their own solutions and
proofs. Besides standard ones, some of the exercises are new and
very interesting. The book contains several simple-to-use
irreducibility criteria for rational polynomials which are not in
any such textbook.This book can also serve as a reference for
professional mathematicians. In particular, it will be a nice book
for PhD students to prepare their qualification exams.
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