The book presents and explains a general, efficient, and elegant method of
approximate solution for boundary value problems for an elliptic system of
partial differential equations arising in elasticity theory
The methodology for constructing generalized Fourier series based on the
structure of the problem is shown in detail, and all the attending
mathematical properties are derived with full rigor
A numerical scheme directly related to the series method is developed and
employed to compute approximate solutions, illustrated by a variety of
examples
This book explains in detail the generalized Fourier series technique for the approximate
solution of a mathematical model governed by a linear elliptic partial differential equation or
system with constant coefficients. The power, sophistication, and adaptability of the method are
illustrated in application to the theory of plates with transverse shear deformation, chosen
because of its complexity and special features. In a clear and accessible style, the authors
show how the building blocks of the method are developed, and comment on the advantages
of this procedure over other numerical approaches. An extensive discussion of the
computational algorithms is presented, which encompasses their structure, operation, and
accuracy in relation to several appropriately selected examples of classical boundary value
problems in both finite and infinite domains. The systematic description of the technique,
complemented by explanations of the use of the underlying software, will help the readers
create their own codes to find approximate solutions to other similar models. The work is
aimed at a diverse readership, including advanced undergraduates, graduate students, general
scientific researchers, and engineers. The book strikes a good balance between the theoretical
results and the use of appropriate numerical applications. The first chapter gives a detailed
presentation of the differential equations of the mathematical model, and of the associated
boundary value problems with Dirichlet, Neumann, and Robin conditions.
Mathematics : Potential Theory
Due 2021-01-12
1st ed. 2020, VIII, 264 p. 186 illus., 37 illus. in color.
Hardcover
ISBN 978-3-030-55848-2
Product category : Monograph
Series : Developments in Mathematics
Structured to allow for concise development of ideas in a classroom setting
Includes chapter-level exercises with solutions available online
Provides proofs and examples throughout each chapter
Aimed at a graduate study level with applications to engineering, researchers,
and graduate-flipped classes
This book is the first volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped
classes. Each volume is divided into short chapters. Each chapter can be covered in one
teaching unit and includes exercises as well as solutions available from a dedicated website.
The salient ideas can be addressed during lecture, with the rest of the content assigned as
reading material. To engage the reader, the text combines examples, basic ideas, rigorous
proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23
chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This
volume focuses on the fundamental ideas regarding the construction of finite elements and
their approximation properties. It addresses the all-purpose Lagrange finite elements, but also
vector-valued finite elements that are crucial to approximate the divergence and the curl
operators. In addition, it also presents and analyzes quasi-interpolation operators and local
commuting projections. The volume starts with four chapters on functional analysis, which are
packed with examples and counterexamples to familiarize the reader with the basic facts on
Lebesgue integration and weak derivatives. Volume I also reviews important implementation
aspects when either developing or using a finite element toolbox, including the orientation of
meshes and the enumeration of the degrees of freedom.
Mathematics : Partial Differential Equations
Due 2020-11-25
1st ed. 2020, XII, 308 p. 52 illus. In 3 volumes, not available separately.
Hardcover
ISBN 978-3-030-56340-0
Product category : Graduate/advanced undergraduate textbook
Series : Texts in Applied Mathematics
Structured to allow for concise development of ideas in a classroom setting
Includes chapter-level exercises with solutions available online
Provides proofs and examples throughout each chapter
This book is the second volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped
classes. Each volume is divided into short chapters. Each chapter can be covered in one
teaching unit and includes exercises as well as solutions available from a dedicated website.
The salient ideas can be addressed during lecture, with the rest of the content assigned as
reading material. To engage the reader, the text combines examples, basic ideas, rigorous
proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32
chapters plus one appendix. The first part of the volume focuses on the approximation of
elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations
and their approximation by the Galerkin method. The material covered includes key results
such as the BNB theorem based on inf-sup conditions, Cea's and Strang's lemmas, and the
duality argument by Aubin and Nitsche. Important implementation aspects regarding
quadratures, linear algebra, and assembling are also covered. The remainder of Volume II
focuses on PDEs where a coercivity property is available. It investigates conforming and
nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix?Raviart,
discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic
PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems
for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix
addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in
Banach spaces.
Due 2020-12-02
1st ed. 2020, IX, 478 p. 24 illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-56922-8
Product category : Graduate/advanced undergraduate textbook
Series : Texts in Applied Mathematics
Short chapters allow for development of ideas in a classroom setting
Many exercises and hints included
Well adapted for graduate flipped classes
Part of a three volume work
This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped
classes. Each volume is divided into short chapters. Each chapter can be covered in one
teaching unit and includes exercises as well as solutions available from a dedicated website.
The salient ideas can be addressed during lecture, with the rest of the content assigned as
reading material. To engage the reader, the text combines examples, basic ideas, rigorous
proofs, and pointers to the literature to enhance scientific literacy. Volume III is divided into 28
chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs
called Friedrichs' systems. This part of the book presents a comprehensive and unified
treatment of various stabilization techniques from the existing literature. It discusses
applications to advection and advection-diffusion equations and various PDEs written in mixed
form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III
addresses time-dependent problems: parabolic equations (such as the heat equation),
evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear
hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh
perspective on the analysis of well-known time-stepping methods. The last five chapters
discuss the approximation of hyperbolic equations with finite elements. Here again a new
perspective is proposed. These chapters should convince the reader that finite elements offer a
good alternative to finite volumes to solve nonlinear conservation equations
Due 2020-12-19
1st ed. 2020, VIII, 407 p. 17 illus.
Hardcover
ISBN 978-3-030-57347-8
Product category : Graduate/advanced undergraduate textbook
Series : Texts in Applied Mathematics
Provides a complete introduction to probability theory, including measure
theory and scientific applications
New updated edition includes concise summaries of each section, as well as
outlooks and questions in the text
Clearly written to make complicated mathematics accessible
This popular textbook, now in a revised and expanded third edition, presents a comprehensive
course in modern probability theory. Probability plays an increasingly important role not only in
mathematics, but also in physics, biology, finance and computer science, helping to understand
phenomena such as magnetism, genetic diversity and market volatility, and also to construct
efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics
in probability, including many not usually found in introductory books, such as: limit theorems
for sums of random variables martingales percolation Markov chains and electrical networks
construction of stochastic processes Poisson point process and infinite divisibility large
deviation principles and statistical physics Brownian motion stochastic integrals and stochastic
differential equations. The presentation is self-contained and mathematically rigorous, with the
material on probability theory interspersed with chapters on measure theory to better illustrate
the power of abstract concepts. This third edition has been carefully extended and includes
new features, such as concise summaries at the end of each section and additional questions
to encourage self-reflection, as well as updates to the figures and computer simulations. With a
wealth of examples and more than 290 exercises, as well as biographical details of key
mathematicians, it will be of use to students and researchers in mathematics, statistics, physics,
computer science, economics and biology
Mathematics : Probability Theory and Stochastic Processes
Due 2020-12-20
3rd ed. 2020, XV, 716 p. 55 illus., 24 illus. in color.
Softcover
ISBN 978-3-030-56401-8
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
Presents an inquiry-based learning approach
Aims to teach probability through games, data, and simulations
Integrates the Julia programming language in-text to write codes for
simulation and data analysis
Includes significant projects at the end of each section for student
collaboration and further study
This undergraduate textbook presents an inquiry-based learning course in stochastic models
and computing designed to serve as a first course in probability. Its modular structure
complements a traditional lecture format, introducing new topics chapter by chapter with
accompanying projects for group collaboration. The text addresses probability axioms leading
to Bayes’ theorem, discrete and continuous random variables, Markov chains, and Brownian
motion, as well as applications including randomized algorithms, randomized surveys, Benford’s
law, and Monte Carlo methods. Adopting a unique application-driven approach to better study
probability in action, the book emphasizes data, simulation, and games to strengthen reader
insight and intuition while proving theorems. Additionally, the text incorporates codes and
exercises in the Julia programming language to further promote a hands-on focus in
modelling. Students should have prior knowledge of single variable calculus. Giray Okten
received his PhD from Claremont Graduate University. He has held academic positions at
University of Alaska Fairbanks, Ball State University, and Florida State University. He received a
Fulbright U.S. Scholar award in 2015. He is the author of an open access textbook in numerical
analysis, First Semester in Numerical Analysis with Julia, published by Florida State University
Libraries, and a co-author of a children’s math book, The Mathematical Investigations of Dr. O
and Arya, published by Tumblehome. His research interests include Monte Carlo methods and
computational finance.
Mathematics : Probability Theory and Stochastic Processes
Due 2020-12-26
1st ed. 2020, X, 116 p. 24 illus., 22 illus. in color.
Softcover
ISBN 978-3-030-56069-0
Product category : Undergraduate textbook
Series : Springer Undergraduate Texts in Mathematics and Technology
Presents a concise, unified account of undergraduate mathematics by
illustrating the rich historical context behind various topics
Balances breadth and rigor in a manageable volume that’s suitable for a onesemester course
Explores various moments in history through a mathematical perspective
This textbook provides a unified and concise exploration of undergraduate mathematics by
approaching the subject through its history. Readers will discover the rich tapestry of ideas
behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology,
and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and
Descartes, this volume offers a glimpse into the broader context in which these ideas
developed, revealing unexpected connections that make this ideal for a senior capstone course.
The presentation of previous versions has been refined by omitting the less mainstream topics
and inserting new connecting material, allowing instructors to cover the book in a onesemester course.
This condensed edition prioritizes succinctness and cohesiveness, and there is
a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As
in previous editions, a wide array of mathematical topics are covered, from geometry to
computation; however, biographical sketches have been omitted. Mathematics and Its History:
A Concise Edition is an essential resource for courses or reading programs on the history of
mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is
assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The
writing is clear, concise and inviting. The style is very different from a traditional text. I found
myself picking it up to read at the expense of my usual late evening thriller or detective
novel…. The author has done a wonderful job of tying together the dominant themes of
undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is
presented in a lively style without unnecessary detail. It is very stimulating and will be
appreciated not only by students. Much attention is paid to problems and to the development
of mathematics before the end of the nineteenth century....
Mathematics : History of Mathematics
Due 2020-12-23
1st ed. 2020, XIII, 391 p. 134 illus., 96 illus. in color.
Hardcover
ISBN 978-3-030-55192-6
Product category : Undergraduate textbook
Series : Undergraduate Texts in Mathematics