Provides application orientated introduction to the numerical methods for
partial differential equations
Examines modern topics, including cell-centered finite volume methods and
methods of convection-dominated problems
Includes detailed illustrations and extensive exercises throughout
This graduate-level text provides an application oriented introduction to the numerical methods
for elliptic and parabolic partial differential equations. It covers finite difference, finite element,
and finite volume methods, interweaving theory and applications throughout. The book
examines modern topics such as adaptive methods, multilevel methods, and methods for
convection-dominated problems and includes detailed illustrations and extensive exercises. For
students with mathematics major it is an excellent introduction to the theory and methods,
guiding them in the selection of methods and helping them to understand and pursue finite
element programming. For engineering and physics students it provides a general framework
for the formulation and analysis of methods. This second edition sees additional chapters on
mixed discretization and on generalizing and unifying known approaches; broader applications
on systems of diffusion, convection and reaction; enhanced chapters on node-centered finite
volume methods and methods of convection-dominated problems, specifically treating the nowpopular
cell-centered finite volume method; and the consideration of realistic formulations
beyond the Poisson's equation for all models and methods.
Due 2021-10-08
2nd ed. 2021, XVI, 802 p. 94 illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-79384-5
Product category : Graduate/advanced undergraduate textbook
Series : Texts in Applied Mathematics
Mathematics : Numerical Analysis
Provides a self-contained introduction to the study of families of slow-fast
systems on surfaces
Contains a unified account of two decades of results on canard cycles
Presents essential techniques in the study of canard phenomena in a precise
and self-contained way
This book offers the first systematic account of canard cycles, an intriguing phenomenon in the
study of ordinary differential equations. The canard cycles are treated in the general context of
slow-fast families of two-dimensional vector fields. The central question of controlling the limit
cycles is addressed in detail and strong results are presented with complete proofs. In
particular, the book provides a detailed study of the structure of the transitions near the critical
set of non-isolated singularities. This leads to precise results on the limit cycles and their
bifurcations, including the so-called canard phenomenon and canard explosion. The book also
provides a solid basis for the use of asymptotic techniques. It gives a clear understanding of
notions like inner and outer solutions, describing their relation and precise structure. The first
part of the book provides a thorough introduction to slow-fast systems, suitable for graduate
students. The second and third parts will be of interest to both pure mathematicians working
on theoretical questions such as Hilbert's 16th problem, as well as to a wide range of applied
mathematicians looking for a detailed understanding of two-scale models found in electrical
circuits, population dynamics, ecological models, cellular (FitzHugh?Nagumo) models,
epidemiological models, chemical reactions, mechanical oscillators with friction, climate models,
and many other models with tipping points.
1st ed. 2021, XXI, 408 p.
101 illus., 42 illus. in color.
Hardcover
ISBN 978-3-030-79232-9
Product category : Monograph
Series : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
/ A Series of Modern Surveys in Mathematics
Mathematics : Dynamical Systems and Ergodic Theory
Simulation and Hierarchical Optimization
Presents results obtained in the first funding phase of the DFG Special
Priority Program on Nonsmooth and Complementarity Based Distributed
Parameter Systems
Aims to establish a theoretical and numerical foundation and develop new
algorithmic paradigms for the treatment of non-smooth phenomena and
associated parameter influences
Considers a wide range of applications, including optimal control of
multiphase fluids, image processing, thermoforming, and the formation of
rivers and networks
Many of the most challenging problems in the applied sciences involve non-differentiable
structures as well as partial differential operators, thus leading to non-smooth distributed
parameter systems. This edited volume aims to establish a theoretical and numerical
foundation and develop new algorithmic paradigms for the treatment of non-smooth
phenomena and associated parameter influences. Other goals include the realization and
further advancement of these concepts in the context of robust and hierarchical optimization,
partial differential games, and nonlinear partial differential complementarity problems, as well
as their validation in the context of complex applications. Areas for which applications are
considered include optimal control of multiphase fluids and of superconductors, image
processing, thermoforming, and the formation of rivers and networks. Chapters are written by
leading researchers and present results obtained in the first funding phase of the DFG Special
Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems:
Simulation and Hierarchical Optimization that ran from 2016 to 2019.
Due 2021-10-03
1st ed. 2021, VIII, 529 p.
Hardcover
ISBN 978-3-030-79392-0
Product category : Contributed volume
Series : International Series of Numerical Mathematics
Mathematics : Optimization
Includes in-text exercises and examples
Presents topics in variational analysis and optimal control to readers without
a background in the field
Provides overview of major developments in an evolving field with
applications to finances and engineering
This book presents an introduction to variational analysis, a field which unifies theories and
techniques developed in calculus of variations, optimization, and control, and covers convex
analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints,
the analysis of which involves set-valued mappings and functions that are not differentiable.
Applications of variational analysis are interdisciplinary, ranging from financial planning to
steering a flying object. The book is addressed to graduate students, researchers, and
practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of
the book should be familiar with multivariable calculus and linear algebra. Some basic
knowledge in optimization, control, and elementary functional analysis is desirable, but all
necessary background material is included in the book.
Due 2021-09-27
1st ed. 2021, XX, 208 p. 13 illus.
Hardcover
ISBN 978-3-030-79910-6
Product category : Monograph
Series : Applied Mathematical Sciences
Mathematics : Optimization
Offers an accessible introduction to the rigorous study of stochastic processes
Builds from simple examples to formal proofs, illuminating key ideas and
computations
Showcases a selection of important contemporary applications, including
mathematical finance, optimal stopping, and ruin theory
This textbook offers an approachable introduction to stochastic processes that explores the
four pillars of random walk, branching processes, Brownian motion, and martingales. Building
from simple examples, the authors focus on developing context and intuition before
formalizing the theory of each topic. This inviting approach illuminates the key ideas and
computations in the proofs, forming an ideal basis for further study. Consisting of many short
chapters, the book begins with a comprehensive account of the simple random walk in one
dimension. From here, different paths may be chosen according to interest. Themes span
Poisson processes, branching processes, the Kolmogorov?Chentsov theorem, martingales,
renewal theory, and Brownian motion. Special topics follow, showcasing a selection of
important contemporary applications, including mathematical finance, optimal stopping, ruin
theory, branching random walk, and equations of fluids. Engaging exercises accompany the
theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to
the rigorous study of stochastic processes. Students and instructors alike will appreciate the
accessible, example-driven approach. A single, graduate-level course in probability is assumed.
Due 2021-09-18
1st ed. 2021, XIII, 400 p.20 illus.
Hardcover
ISBN 978-3-030-78937-4
Product category : Graduate/advanced undergraduate textbook
Series : Graduate Texts in Mathematics
Mathematics : Probability Theory and Stochastic Processes
LMS-CMI Research School, London, July 2018
Presents the state of the art in applications of homotopy theory to arithmetic
geometry
A unique collection of original lecture notes aimed at research students
Contains lectures on etale and motivic homotopy theory, arithmetic
enumerative geometry, and motives
This book provides an introduction to state-of-the-art applications of homotopy theory to
arithmetic geometry. The contributions to this volume are based on original lectures by leading
researchers at the LMS-CMI Research School on eHomotopy Theory and Arithmetic Geometry -
Motivic and Diophantine Aspectsf and the Nelder Fellow Lecturer Series, which both took place
at Imperial College London in the summer of 2018. The contribution by Brazelton, based on
the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the
notes of Cisinski present motivic sheaves and new cohomological methods for intersection
theory, and Schlankfs contribution gives an overview of the use of etale homotopy theory for
obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok
and Ostvar, based in part on the Nelder Fellow lecture series by Ostvar, gives a survey of the
interplay between motivic homotopy theory and affine algebraic geometry, with a focus on
contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a
detailed guide to the fascinating circle of recent applications of homotopy theory to number
theory. It will be invaluable to research students entering the field, as well as postdoctoral and
more established researchers.
Due 2021-10-08
1st ed. 2021, IX, 218 p.
Softcover
ISBN 978-3-030-78976-3
Product category : Contributed volume
Series : Lecture Notes in Mathematics
Mathematics : Algebraic Geometry
Provides a comprehensive account of linear and non-linear state space
modelling, including R
Discusses in detail the applications to financial time series, dynamic systems,
and control
Reviews simulation-based Bayesian inference, such as Markov chain Monte
Carlo and sequential Monte Carlo methods
Demonstrates how state space modelling can be applied using R
Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a
comprehensive introduction to Bayesian estimation and forecasting for state space models. The
celebrated Kalman filter, with its numerous extensions, takes centre stage in the book.
Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are
discussed with applications to signal processing, environmetrics, economics and systems
engineering. Over the past years there has been a growing literature on Bayesian inference of
state space models, focusing on multivariate models as well as on non-linear and nonGaussian
models. The availability of time series data in many fields of science and industry on
the one hand, and the development of low-cost computational capabilities on the other, have
resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This
book brings together many of these methods, presenting an accessible and comprehensive
introduction to state space models. A number of data sets from different disciplines are used
to illustrate the methods and show how they are applied in practice. The R package BTSA,
created for the book, includes many of the algorithms and examples presented. The book is
essentially self-contained and includes a chapter summarising the prerequisites in
undergraduate linear algebra, probability and statistics. An up-to-date and complete account of
state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a
wide range of students and scientists, notably in the disciplines of statistics, systems
engineering, signal processing, data science, finance and econometrics.
Due 2021-11-03
1st ed. 2021, X, 477 p. 87 illus., 33 illus. in color.
Hardcover
ISBN 978-3-030-76123-3
Product category : Graduate/advanced undergraduate textbook
Series : Springer Texts in Statistics
Statistics : Statistics (general)
Makes a long sequence of papers considerably more accessible
Gives a corrected new proof of an influential result of Hung
Contains applications to the existence of k-regular maps
This book gives a brief treatment of the equivariant cohomology of the classical configuration
space F(^d,n) from its beginnings to recent developments. This subject has been studied
intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and
progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and
Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F
(^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure
was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main
theorem is given, however it is shown that some of the arguments given by him on the way to
his result are incorrect, as are some of the intermediate results in his paper. This invalidates a
paper by three of the authors, Blagojevi, Luck and Ziegler (2016), who used a claimed
intermediate result in order to derive lower bounds for the existence ofk-regular and -skew
embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence
of highly regular embeddings are obtained: Some of them agree with the previously claimed
bounds, some are weaker. Assuming only a standard graduate background in algebraic
topology, this book carefully guides the reader on the way into the subject. It is aimed at
graduate students and researchers interested in the development of algebraic topology in its
applications in geometry.
Due 2021-10-23
1st ed. 2021, X, 196 p. 12 illus.
Softcover
ISBN 978-3-030-84137-9
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Algebraic Topology