|
Books > Science & Mathematics > Mathematics
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.
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.
500 Ways to Achieve Your Highest Score
We want you to succeed on the Math sections of the ACT. That's
why we've selected these 500 questions to help you study more
effectively, use your preparation time wisely, and get your best
score. These questions are similar to the ones you'll find on the
ACT, so you will know what to expect on test day. Each question
includes a concise, easy-to-follow explanation in the answer key
for your full understanding of the concepts. Whether you have been
studying all year or are doing a last-minute review, "McGraw-Hill's
500 ACT Math Questions to Know by Test Day" will help you achieve
the high score you desire.
Sharpen your subject knowledge, and build your test-taking
confidence with: 500 ACT Math questions Full explanations for each
question in the answer key A format parallel to that of the ACT
exam
Perfect and amicable numbers, as well as a majority of classes of
special numbers, have a long and rich history connected with the
names of many famous mathematicians. This book gives a complete
presentation of the theory of two classes of special numbers
(perfect numbers and amicable numbers) and gives much of their
properties, facts and theorems with full proofs of them, as well as
their numerous analogue and generalizations.
This study guide for Varsity Maths Preparation has been compiled by
Emeritus Professor John Webb in response to the dire challenges
experienced by first year university students, in Mathematics as
well as in courses in Science, Engineering and Business Science,
all heavily dependent on mathematical thinking. By working through
the problem sets in this self-study book, learners should develop
and test their skills, on their own, in areas such as algebraic
expertise, trigonometry skills, word problems, geometric insight,
numerical facility, logical reasoning and flexible thinking. This
cannot be taught and is best achieved without assistance and
timeously, i.e. prior to students entering university. The
problem-solving techniques which learners could acquire from
dedicated, independent use of this outstanding booklet will
contribute significantly to their success in the National Benchmark
tests (NBTs). Varsity Maths Prep is a gem for learners who are
serious about an academic future.
|
|