Format: Hardback, 160 pages, height x width: 240x168 mm, 1 Illustrations, black and white
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 25-May-2026
ISBN-13: 9783032227119
This book is intended as a bridge between high school and college mathematics. The contents have been chosen to demonstrate the relationships among topics from the high school curriculum, including topics that may be part of a fourth year non-calculus mathematics course and first and second year college courses. As the title indicates, the common thread of this work is the linear function. The two parts of the book are devoted, in turn, to: the linear function of a real variable and the linear function of a 2-dimensional vector variable. A second common thread is the visualization of these functions as transformations of 1- or 2-dimensional Euclidean space. The topics, examples, and problems have all been chosen to encourage the integration of the major topics from the high school curriculum. Another feature of this book is that it includes proofs. Specifically, not the formal two column proofs often included in the study of geometry in high school, but the more informal, but nevertheless rigorous, step-by-step explanations of why what we believe to be true is indeed true. One of the common complaints of the colleges is that a large majority of incoming freshmen do not have algebra as a usable tool. In this book, algebra is seen to be an essential tool for the further study of mathematics. Algebraic skills are strengthened by constantly using algebra and by seeing the application of algebra in a variety of settings.
Preface.- Introduction.- The Geometry of the Euclidean Line.- Linear
Difference Equations.- The Mathematics of Personal Finance.- Linear Functions
in Business.- Research Projects.- Affine Geometry.- Matrix
Algebra.- Euclidean Geometry.
Format: Hardback, 520 pages, height x width: 235x155 mm, 8 Illustrations, black and white
Series: Problem Books in Mathematics
Pub. Date: 10-Jun-2026
ISBN-13: 9783032177100
Presenting a rich collection of exercises on partial differential equations, this textbooknow in its second editionequips readers with over 600 examples, exercises, and problems, complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented scientific fields, from physics and engineering to differential geometry and variational calculus. New in this edition is the examination of models in physics that can be described by partial differential equations, including those in diffusion, acoustics, quantum mechanics, electromagnetism, and more. A new section is devoted to the use of distributions, or generalized functions, with a focus on the highly useful delta function. Additional problems and examples have been included, along with an expanded bibliography.
Thoughtfully organized into eight chapters, plus two additional chapters with solutions, the journey begins with fundamental problems in the realm of PDEs. Readers progress through first- and second-order equations, wave and heat equations, and finally, the Laplace equation. The text adopts a highly readable and mathematically rigorous format, ensuring that concepts are introduced with clarity and structure.
Designed to cater to upper undergraduate and graduate students, this book offers a comprehensive understanding of partial differential equations. Researchers and practitioners seeking to strengthen their problem-solving skills will also find this exercise collection both challenging and beneficial.
General introduction.- The physical origins of partial differential
equations.- First-order partial differential equations.- Classifications of
second-order partial differential equations.- Classifications and canonical
forms for linear second-order partial differential equations.- The Laplace
equation.- The heat equation.- The wave equation.- Solutions, hints, and
answers to the exercises.- Solutions, hints, and answers to the problems.-
Bibliography.- Inde
Format: Hardback, 343 pages, height x width: 235x155 mm, XIV, 343 p.
Pub. Date: 07-Jun-2026
ISBN-13: 9789819577613
This book presents the latest international research achievements in complex chaotic systems, establishing itself as an reference with high value in nonlinear dynamics and chaos theory. The book systematically explores dynamical behaviors of complex chaotic systems through control methods and engineering technologies, with particular emphasis on chaos synchronization and its revolutionary applications in secure communication. It introduces chaos synchronization including anti-synchronization, projective synchronization, hybrid projective synchronization, and various advanced synchronization techniques for both integer-order and fractional-order complex chaotic systems. Furthermore, the work demonstrates pioneering applications of chaotic systems and synchronization technologies in the field of secure communication. This publication stands out through its comprehensive pedagogical features, which include detailed mathematical frameworks and illustrative case studies. The content is strategically organized to guide readers progressively from fundamental concepts in Chapter 1, through various synchronization types of integer-order systems in Chapters 2-12, followed by in-depth analysis of fractional-order systems in Chapters 13-18, and culminating with practical encryption applications in the final chapters. The principal merit of this work resides in its distinctive integration of theoretical rigor and practical applicability, providing readers with both foundational comprehension and executable methodologies for complex system analysis. It serves not only as an essential reference resource for secure communication but also establishes a solid theoretical foundation and offers innovative methodological pathways for researchers exploring complex systems.
Introduction and Preliminary Knowledge.- Anti-synchronization of complex
chaotic systems.
Format: Hardback, 667 pages, height x width: 235x155 mm, 50 Illustrations, color; 17 Illustrations, black and white
Series: Graduate Texts in Physics
Pub. Date: 03-Jun-2026
ISBN-13: 9783032211187
This graduate-level textbook covers the essential concepts and applications of quantum mechanics. Suitable for a one-year core course, it provides a comprehensive and modern treatment, with a focus on pedagogical clarity and abundant derivations and worked examples. The text starts by reviewing the experiments that motivated the quantum revolution, then gives a concise explanation of the requisite mathematical tools, the core postulates of quantum mechanics, and the quantum version of the Noether principle relating symmetries to conserved quantities and selection rules. In addition to the usual standard topics, it covers the coherent states of the harmonic oscillator, Landau levels for a particle in a magnetic field, unbound states for Coulomb potentials, the Wigner-Eckart theorem, entanglement, the Einstein-Podolsky-Rosen problem, hidden variables theories, Bell inequalities, Aspect experiments, vibrational and rotational states of simple molecules, Bloch wavefunctions and periodic potentials, absorption and emission of light, subsystems and open systems, generalized measurements, the Lindblad equation, decoherence, the basics of quantum information, the Dirac equation, the Feynman path integral approach, and the Aharonov-Bohm effect. Exercises are included at the end of each chapter.
Introduction the Quantum Revolution.- Math Tools States Operators and
Representations.- The Core Principles of Quantum Mechanics.- Canonical
Variables and the Hamiltonian.- Transformations Symmetries and Conservation
Laws.- Particle Moving in One Dimension.- The Harmonic Oscillator.- Angular
Momentum and Its Representations.- Charged Particle in a Magnetic Field.-
Examples with Spherical Symmetry.- Coulomb Potential and Hydrogen Like
Atoms.- Addition of Angular Momenta.- Tensor Operators and Useful Rules They
Obey.- Entanglement the EPR Problem Hidden Variables and Bell Inequalities.-
Stationary State Perturbation Theory.- The Variational Method.- Fine
Hyperfine and Magnetic Effects for the Hydrogen Atom.- Identical Particles
and Multi Electron Atoms.- Periodic Potentials.- Simple Molecules.-
Heisenberg and Interaction Representations.- Time Dependent Perturbation
Theory.- Absorption and Emission of Light.- Scattering in Three Dimensions.-
Subsystems Entanglement Evolution and Generalized Measurements.-
Decoherence.- Invitation to Quantum Information.- Relativistic Quantum
Mechanics.- Feynman Path Integral Approach.
Format: Hardback, 264 pages, height x width: 235x155 mm, X, 264 p.
Series: CMS/CAIMS Books in Mathematics
Pub. Date: 07-Jun-2026
ISBN-13: 9783032204813
This thoroughly updated second edition offers a unified, modern pathway from the Kolmogorov foundations of probability to the tools of stochastic calculusand on to applications in finance, statistics, and risk. With clarity and breadth, it develops martingale and semimartingale theory alongside stochastic differential equations, keeping both discrete- and continuous-time viewpoints in play.
Whats new in the 2nd Edition
Optional Stochastic Analysis on non-usual filtrations: the first textbook presentation of optional processes on stochastic bases beyond the standard right-continuous, complete setting, with an accompanying optional stochastic calculus. Optional SDEs and stochastic exponentials/logarithms: existence-uniqueness theory and product/inverse rules, with financial modeling worked out in this optional-semimartingale framework. New applications: Stochastic Regression Analysis and Risk Theory, showing how optional tools yield estimation results and ruin-probability bounds in general settings. Expanded exercises with solutions: a substantially enlarged Supplement (Ch. 15) featuring problems that reinforce both core theory and applications.
Designed for senior undergraduates, graduate students, and instructors, the book also serves researchers and practitioners who need a concise, example-driven route from measure-theoretic probability to the techniques used in finance, statistics, and risk modeling. Abundant worked examples and a comprehensive set of problemswith hints and solutionsmake it ideal for self study or course adoption.
Probabilistic Foundations.- Random variables and their quantitative
characteristics.- Expectations and convergence of sequences of random
variables.- Weak convergence of sequences of random variables.- Absolute
continuity of probability measures and conditional expectations.- Discrete
time stochastic analysis: basic results.- Discrete time stochastic analysis:
further results and applications.- Elements of classical theory of stochastic
processes.- Stochastic differential equations, diffusion processes and their
applications.- General theory of stochastic processes under usual
conditions".- General theory of stochastic processes in applications.- Basic
elements of optional stochastic analysis.- Optional stochastic differential
equations and their applications.- Optional semimartingales for stochastic
regression analysis and risk theory.- Supplementary problems.
Format: Hardback, 371 pages, height x width: 279x210 mm, XII, 371 p.
Pub. Date: 06-Jun-2026
ISBN-13: 9783032233271
This book offers a unified and rigorous treatment of nonlinear differential equations involving the Caputo tempered fractional derivative and its generalizations. Spanning nine chapters, the authors systematically develop analytical methods for solving a wide variety of problems, including those with nonlocal, impulsive, periodic and delayed structures, within both deterministic and random settings. Each chapter is dedicated to a particular class of problems, beginning with global convergence and uniqueness analysis for the successive approximations method and extending to systems with neutral and infinite delays, boundary value problems with impulses, and coupled systems. The analytical approaches employed throughout the book include a rich array of mathematical tools: fixed point theory (Banach, Schauder, Darbo, Monch, Schaefer, Sadovskii, and Krasnoselskii); coincidence degree theory; the method of upper and lower solutions; diagonalization techniques; and the measure of noncompactness. Special attention is given to various notions of stability, including Ulam-Hyers and Mittag-Leffler-Ulam-Hyers stability, as well as the existence of periodic and weak solutions. To ensure practical relevance and illustrate the applicability of each theoretical result, every chapter concludes with a section devoted to remarks and bibliographical suggestions as well as examples that highlight the effectiveness of the proposed methods. This book is ideal for graduate students, researchers, and professionals working in the fields of applied mathematics, differential equations, and fractional calculus.
Introduction.- Preliminary Background.- Fractional Operators.- Measure
of Noncompactness.- Different Approaches and Employed Methods.- Quantitative
Study on Caputo Type Tempered Fractional Differential Equations.- Caputo
Tempered Fractional Differential Equations with Delay.- Existence and
Oscillatory Results of Caputo Tempered Fractional Differential Equations.-
Caputo Tempered Fractional Differential Equations in b-Metric Spaces.- Caputo
Tempered Fractional Periodic Problems.- Tempered (k,)-Hilfer Fractional
Problems.- Bibliography.- Index.
Format: Hardback, 220 pages, height x width: 235x155 mm, I, 220 p.
Series: Tohoku Series in Mathematical Sciences
Pub. Date: 08-Jun-2026
ISBN-13: 9789819581603
This proceedings volume is the first of a two-volume set collecting original papers by invited speakers and participants of the international conference Critical Phenomena in Nonlinear Partial Differential Equations, Harmonic Analysis, and Functional Inequalities, held at the Sendai International Center in November 2023. The aim of the conference was to showcase recent progress in the study of nonlinear partial differential equations, harmonic analysis, and functional inequalities, with a particular focus on critical phenomena. Topics discussed during the conference include global well-posedness for nonlinear PDEs arising in fluid mechanics, long-time behavior of solutions to chemotaxis systems, scattering problems for nonlinear dispersive equations, and the sharpness and attainability of functional inequalities, among others. This volume aims to share these developments with a broader mathematical audience, offering insights into current research trends and techniques in the field.
Preface.- Biographical Sketch and Academic Career of Takayoshi Ogawa.-
Some consequences of the sharp Euclidean logarithmic Sobolev inequality with
monomial weight.- Uniqueness of almost periodic-in-time solutions to the
Boussinesq system in unbounded domains.- $L^p$ estimate of the heat equation
on a bounded domain.- A note on strong instability of standing waves for
nonlinear SchrØodinger equations with double power nonlinearity.
Format: Hardback, 301 pages, height x width: 235x155 mm, 74 Illustrations, color
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 19-May-2026
ISBN-13: 9789819592104
The Siddhntairomai was composed in 1150 CE by the celebrated mathematicianastronomer Bhskarcrya. In the Grahagaitdhyya part of it, most of the standard calculations and algorithms in Indian astronomy of his times are included. All these are explained in detail with commentary on the text, namely, the Vsanbhya or Mitkar. This book is on this part only. All the 460 verses of this part have been translated afresh in this work. Now, it is in the Vsanbhya that the contents of the verses are expounded in detail. In addition, the detailed derivations and proofs of the statements and algorithms are presented in the upapattis. Study of the vsan is indispensable for understanding the methodology of, in particular, and thereby, of Indian astronomers in general. The distinct scientific method of Bhskara (indeed of the Indian astronomical tradition in general, of which he was a leading exponent), his approach to problems and the ways to solve them, can be understood only when one goes through the commentary and understands it. It is for this reason that the Vsanbhya has been translated into English for all the verses, for the first time. Explanatory notes based on the vsan of Bhskara have been provided for all the verses in modern notation, with a large number of diagrams to facilitate the understanding. The Grahagaitdhyya has 12 chapters, which is divided into two volumes: Volume 1: Madhyama, Spaa, Triprana and Volume 2: Parvasambhava to Pta Adhikras. Volume 1 has three chaptersthe Madhyamdhikra, Spadhikra and the Triprandhikra. This volume has a comprehensive introduction and two appendices on the Indian planetary model and elements of spherical trigonometry, which make this book reasonably self-contained. Volume 2 has the nine chaptersParvasambhava, Candragrahaa, Sryagrahaa, Grahacchy, Udaysta, gonnati, Grahayuti, Bhagrahayuti and the Pta adhikras.
Chapter Possibility of Eclipses.
Chapter Lunar eclipse.
Chapter Solar eclipse.
Chapter Shadow of a planet.
Chapter (Heliacal) Rising and Settting of Planets.
Chapter Elevation of the lunar cusps.
Chapter Conjunctions of planets.
Chapter Conjunction of a star and a planet.
Chapter Equal declinations of the Sun and the Moon.