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Books > Science & Mathematics > Mathematics
Nonlinear Time Series Analysis with R provides a practical guide to
emerging empirical techniques allowing practitioners to diagnose
whether highly fluctuating and random appearing data are most
likely driven by random or deterministic dynamic forces. It joins
the chorus of voices recommending 'getting to know your data' as an
essential preliminary evidentiary step in modelling. Time series
are often highly fluctuating with a random appearance. Observed
volatility is commonly attributed to exogenous random shocks to
stable real-world systems. However, breakthroughs in nonlinear
dynamics raise another possibility: highly complex dynamics can
emerge endogenously from astoundingly parsimonious deterministic
nonlinear models. Nonlinear Time Series Analysis (NLTS) is a
collection of empirical tools designed to aid practitioners detect
whether stochastic or deterministic dynamics most likely drive
observed complexity. Practitioners become 'data detectives'
accumulating hard empirical evidence supporting their modelling
approach. This book is targeted to professionals and graduate
students in engineering and the biophysical and social sciences.
Its major objectives are to help non-mathematicians - with limited
knowledge of nonlinear dynamics - to become operational in NLTS;
and in this way to pave the way for NLTS to be adopted in the
conventional empirical toolbox and core coursework of the targeted
disciplines. Consistent with modern trends in university
instruction, the book makes readers active learners with hands-on
computer experiments in R code directing them through NLTS methods
and helping them understand the underlying logic (please see
www.marco.bittelli.com). The computer code is explained in detail
so that readers can adjust it for use in their own work. The book
also provides readers with an explicit framework - condensed from
sound empirical practices recommended in the literature - that
details a step-by-step procedure for applying NLTS in real-world
data diagnostics.
This book contains an extensive illustration of use of finite
difference method in solving the boundary value problem
numerically. A wide class of differential equations has been
numerically solved in this book. Starting with differential
equations of elementary functions like hyperbolic, sine and cosine,
we have solved those of special functions like Hermite, Laguerre
and Legendre. Those of Airy function, of stationary localised
wavepacket, of the quantum mechanical problem of a particle in a 1D
box, and the polar equation of motion under gravitational
interaction have also been solved. Mathematica 6.0 has been used to
solve the system of linear equations that we encountered and to
plot the numerical data. Comparison with known analytic solutions
showed nearly perfect agreement in every case. On reading this
book, readers will become adept in using the method.
Uncertainties in GPS Positioning: A Mathematical Discourse
describes the calculations performed by a GPS receiver and the
problems associated with ensuring that the derived location is a
close match to the actual location. Inaccuracies in calculating a
location can have serious repercussions, so this book is a timely
source for information on this rapidly evolving technology.
Mathematics for Neuroscientists, Second Edition, presents a
comprehensive introduction to mathematical and computational
methods used in neuroscience to describe and model neural
components of the brain from ion channels to single neurons, neural
networks and their relation to behavior. The book contains more
than 200 figures generated using Matlab code available to the
student and scholar. Mathematical concepts are introduced hand in
hand with neuroscience, emphasizing the connection between
experimental results and theory.
First Semester Calculus for Students of Mathematics and Related
Disciplines equips students with a strong working knowledge of the
fundamental principles of calculus, providing an engaging and
accessible entry point into this critical field of study. It
prepares students for more advanced courses in calculus and also
helps them understand how to apply basic principles of calculus to
solve problems within a wide range of disciplines, including
business, biology, engineering, science, liberal arts and, of
course, mathematics. The text employs rigorous treatment of early
calculus topics and detailed explanations to facilitate deeper
understanding of later material. Over the course of five chapters,
students learn about symbolic logic, continuity and limits,
derivatives, antiderivatives, and applications of each. Throughout,
students are provided with rich guidance and copious opportunities
to deepen their personal understanding of the subject matter. In
the second edition, a more efficient layout better highlights major
theorems and definitions. Additionally, over 300 new exercises have
been added to further aid student learning. Highly readable and
innovative, yet pedagogically solid and very applicable, First
Semester Calculus for Students of Mathematics and Related
Disciplines is an ideal resource for a variety of courses that
apply concepts of calculus to solve mathematical and real-world
problems.
INTRODUCTION TO LINEAR REGRESSION ANALYSIS A comprehensive and
current introduction to the fundamentals of regression analysis
Introduction to Linear Regression Analysis, 6th Edition is the most
comprehensive, fulsome, and current examination of the foundations
of linear regression analysis. Fully updated in this new sixth
edition, the distinguished authors have included new material on
generalized regression techniques and new examples to help the
reader understand retain the concepts taught in the book. The new
edition focuses on four key areas of improvement over the fifth
edition: New exercises and data sets New material on generalized
regression techniques The inclusion of JMP software in key areas
Carefully condensing the text where possible Introduction to Linear
Regression Analysis skillfully blends theory and application in
both the conventional and less common uses of regression analysis
in today's cutting-edge scientific research. The text equips
readers to understand the basic principles needed to apply
regression model-building techniques in various fields of study,
including engineering, management, and the health sciences.
For a physicist, "noise" is not just about sounds, but refers to
any random physical process that blurs measurements, and in so
doing stands in the way of scientific knowledge. This book deals
with the most common types of noise, their properties, and some of
their unexpected virtues. The text explains the most useful
mathematical concepts related to noise. Finally, the book aims at
making this subject more widely known and to stimulate the interest
for its study in young physicists.
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