Highlights an unprecedented number of real-life applications of differential
equations and systems
Includes problems in biomathematics, finance, engineering, physics, and even
societal ones like rumors and love
Includes selected challenges to motivate further research in this field
This book highlights an unprecedented number of real-life applications of differential equations
together with the underlying theory and techniques. The problems and examples presented
here touch on key topics in the discipline, including first order (linear and nonlinear) differential
equations, second (and higher) order differential equations, first order differential systems, the
Runge?Kutta method, and nonlinear boundary value problems. Applications include growth of
bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the
shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood
vessels, price-demand-supply relations, predator-prey relations, and many more. Upper
undergraduate and graduate students in Mathematics, Physics and Engineering will find this
volume particularly useful, both for independent study and as supplementary reading. While
many problems can be solved at the undergraduate level, a number of challenging real-life
applications have also been included as a way to motivate further research in this vast and
fascinating field
Hardcover
ISBN 978-3-030-26383-6
Product category : Undergraduate textbook
Series : Problem Books in Mathematics
Mathematics : Ordinary Differential Equations
Introduces new framework for nonautonomous dynamical systems
Develops theoretical foundations of impulsive functional differential
equations, including linear and nonlinear systems, stability, and invariant
manifold theory
Spotlights recent advances in stability and bifurcation
Contains detailed calculations to support application-driven approach
Delivers material in self-contained, three-part structure
This monograph presents the most recent progress in bifurcation theory of impulsive
dynamical systems with time delays and other functional dependence. It covers not only
smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique
to impulsive dynamical systems. The monograph is split into four distinct parts, independently
addressing both finite and infinite-dimensional dynamical systems before discussing their
applications. The primary contributions are a rigorous nonautonomous dynamical systems
framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special
attention is paid to the centre manifold and associated reduction principle, as these are
essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is
extended to impulsive functional differential equations, and this permits an exploration of the
impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will
learn how techniques of classical bifurcation theory extend to impulsive functional differential
equations and, as a special case, impulsive differential equations without delays. They will learn
about stability for fixed points, periodic orbits and complete bounded trajectories, and how the
linearization of the dynamical system allows for a suitable definition of hyperbolicity.
Due 2021-04-14
1st ed. 2021, X, 356 p. 29
illus., 12 illus. in color.
Hardcover
ISBN 978-3-030-64532-8
Product category : Monograph
Series : IFSR International Series in Systems
Science and Systems Engineering
Mathematics : Dynamical Systems and Ergodic Theory
Explores the foundations of real analysis using the framework of general
ordered fields, demonstrating the multifaceted nature of the area
Illustrates the definitions and logical interrelations between core concepts of
real analysis, using numerous examples and counterexamples
Presents the material in a self-contained manner, featuring three appendices
and over 130 exercises
This textbook explores the foundations of real analysis using the framework of general ordered
fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of
real analysis, the definitions and interrelations between core concepts are illustrated with the
use of numerous examples and counterexamples. Readers will learn of the equivalence
between various theorems and the completeness property of the underlying ordered field.
These equivalences emphasize the fundamental role of real numbers in analysis. Comprising
six chapters, the book opens with a rigorous presentation of the theories of rational and real
numbers in the framework of ordered fields. This is followed by an accessible exploration of
standard topics of elementary real analysis, including continuous functions, differentiation,
integration, and infinite series. Readers will find this text conveniently self-contained, with three
appendices included after the main text, covering an overview of natural numbers and integers,
Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real
Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate
level who are interested in the logical underpinnings of real analysis. With over 130 exercises,
it is suitable for a one-semester course on elementary real analysis, as well as independent
study
1st ed. 2021, XII, 178 p. 13 illus.
Softcover
ISBN 978-3-030-64700-1
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
Mathematics : Real Functions
Provides a set of results concerning nonlinear Schrodinger equations in the
whole space driven by fractional operators
Deals with fractional Schrodinger equations involving different type of
potentials and nonlinearities satisfying certain growth assumptions
Addressed to researchers interested in pure and applied mathematics,
physics, mechanics, and engineering
This monograph presents recent results concerning nonlinear fractional elliptic problems in the
whole space. More precisely, it investigates the existence, multiplicity and qualitative properties
of solutions for fractional Schrodinger equations by applying suitable variational and
topological methods. The book is mainly intended for researchers in pure and applied
mathematics, physics, mechanics, and engineering. However, the material will also be useful for
students in higher semesters and young researchers, as well as experienced specialists
working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear
Schrodinger equations by applying variational and topological methods
1st ed. 2021, X, 576 p.
Softcover
ISBN 978-3-030-60219-2
Product category : Monograph
Series : Frontiers in Elliptic and Parabolic Probl
Mathematics : Analysis
Presents important contributions to modern theories concerning the
distribution theory applied to convex analysis
Includes approximate formulations of variation problems, such as the
Galerkin method or the finite element method
Is useful for those who use mathematics to solve engineering and physics
problems
This book presents important contributions to modern theories concerning the distribution
theory applied to convex analysis (convex functions, functions of lower semicontinuity, the
subdifferential of a convex function). The authors prove several basic results in distribution
theory and present ordinary differential equations and partial differential equations by providing
generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects
related to variation problems, such as the Stokes system, the elasticity system and the plate
equation. The authors also include approximate formulations of variation problems, such as the
Galerkin method or the finite element method. The book is accessible to all scientists, and it is
especially useful for those who use mathematics to solve engineering and physics problems.
The authors have avoided concepts and results contained in other books in order to keep the
book comprehensive. Furthermore, they do not present concrete simplified models and pay
maximal attention to scientific rigor.
1st ed. 2021, VIII, 276 p. 1illus.
Hardcover
ISBN 978-3-030-67158-7
Product category : Monograph
Mathematics : Probability Theory and Stochastic Processes
Explains the motivations behind concepts as they arise, often comparing them
to their counterparts in other areas of mathematics
Includes foundational concepts from commutative algebra and details their
origins. The concept of regularity is one key example
Shows readers a path toward more advanced concepts, which is what serious
students need today
The goal of this book is to provide an introduction to algebraic geometry accessible to
students. Starting from solutions of polynomial equations, modern tools of the subject soon
appear, motivated by how they improve our understanding of geometrical concepts. In many
places, analogies and differences with related mathematical areas are explained. The text
approaches foundations of algebraic geometry in a complete and self-contained way, also
covering the underlying algebra. The last two chapters include a comprehensive treatment of
cohomology and discuss some of its applications in algebraic geometry
Due 2021-03-25
1st ed. 2021, XX, 470 p.
Softcover
ISBN 978-3-030-62643-3
Product category : Graduate/advanced undergraduate textbook
Mathematics : Algebraic Geometry
Challenges students ranging from high school to graduate levels to develop
problem-solving skills in analytic number theory
Balances elementary yet ingenious problems with applications not usually
seen in classes
Suitable as a rich supplementary text in Analytic Number Theory for
undergraduate and graduate courses
This problem book gathers together 15 problem sets on analytic number theory that can be
profitably approached by anyone from advanced high school students to those pursuing
graduate studies. It emerged from a 5-week course taught by the first author as part of the
2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While
it is recommended that the reader has a solid background in mathematical problem solving (as
from training for mathematical contests), no possession of advanced subject-matter knowledge
is assumed. Most of the solutions require nothing more than elementary number theory and a
good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic
functions, the distribution of prime numbers, the distribution of squares and nonsquares
modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more.
This book is suitable for any student with a special interest in developing problem-solving skills
in analytic number theory. It will be an invaluable aid to lecturers and students as a
supplementary text for introductory Analytic Number Theory courses at both the undergraduate
and graduate level.
1st ed. 2021, XIII, 197 p. 3 illus.
Hardcover
ISBN 978-3-030-65076-6
Product category : Undergraduate textbook
Series : Problem Books in Mathematics
Mathematics : Number Theory
Suggestions for people between 9 and 99 years to look at and explore
The book offers a wealth of material and suggestions for research,
experimentation and investigation from a wide range of mathematical fields
Almost no knowledge is required, only curiosity about own discoveries and
thoughts
It is suitable as a gift, as a resource for teachers interested in mathematics or
as a prize in mathematics competitions
In 17 chapters, this book attempts to deal with well-known and less well-known topics in
mathematics. This is done in a vivid way and therefore the book contains a wealth of colour
illustrations. It deals with stars and polygons, rectangles and circles, straight and curved lines,
natural numbers, square numbers and much more. If you look at the illustrations, you will
discover plenty of exciting and beautiful things in mathematics. The book offers a variety of
suggestions to think about what is depicted and to experiment in order to make and check
your own assumptions. For many topics, no (or only few) prerequisites from school lessons are
needed. It is an important concern of the book that young people find their way to
mathematics and that readers whose school days are some time ago discover new things. The
numerous references to internet sites and further literature help in this respect. "Solutions" to
the suggestions interspersed in the individual sections can be downloaded from the Springer
website. The book was thus written for everyone who enjoys mathematics or who would like to
understand why the book bears this title. It is also aimed at teachers who want to give their
students additional or new motivation to learn. This book is a translation of the original
German 2nd editionMathematik ist schonby Heinz Klaus Strick, published by Springer-Verlag
GmbH, DE, part of Springer Nature in 2019. The translation was done with the help of artificial
intelligence (machine translation by the service DeepL.com). In the subsequent editing, the
author, with the friendly support of John O'Connor, St Andrews University, Scotland, tried to
make it closer to a conventional translation. Still, the book may read stylistically differently
from a conventional translation.
Due 2021-03-15
1st ed. 2021, XI, 252 p. 67 illus.
Softcover
ISBN 978-3-662-62688-7
Product category : Popular science
Mathematics : Mathematics (general)