Format: Hardback, 425 pages, height x width: 235x155 mm, 48 Illustrations, black and white
Series: Texts in Applied Mathematics
Pub. Date: 22-Dec-2025
ISBN-13: 9783032084002
This is the third and final volume of Mathematical Systems Theory. Like the preceding volumes, it presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed, and mathematically rigorous manner. The exposition proceeds from the very general to the more specific, with rigorous mathematics complemented by numerous illustrations and explanatory remarks.
Volume III comprises two chapters and an appendix. In contrast to the first two volumes, only continuous-time systems are considered here. Chapter 9 addresses linear-quadratic optimal control and the Riccati equation, while Chapter 10 deals with zero dynamics and adaptive feedback regulation. Distinctive features include:
a comprehensive treatment of the linear-quadratic optimal control problem
Linear Quadratic Optimal Control and the Riccati Equation.- Zero
Dynamics and Adaptive Feedback Regulation.- References.- Glossary.- Index .
Format: Paperback / softback, 269 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Series: Springer Undergraduate Mathematics Series
Pub. Date: 12-Jan-2026
ISBN-13: 9781447176091
Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The treatment relies heavily on the convergence properties of sequences and series of numbers as well as functions and assumes a solid background in advanced calculus and an acquaintance with ordinary differential equations and linear algebra. The presentation follows a clear and rigorous mathematical style that is both readable and well-motivated, with many examples and applications used to illustrate the theory.
Intended for a one-semester undergraduate course, the book includes numerous exercises, with solutions to selected exercises provided and a full solutions manual available for course instructors. Although addressed primarily to undergraduate students of mathematics, the book will also be of interest to students in related disciplines, such as physics and engineering, where Fourier analysis and special functions are used extensively for solving linear differential equations. Familiarity with the relevant theorems of real analysis, such as the Ascoli-Arzela theorem and the dominated convergence theorem, are also useful for following the proofs.
Format: Hardback, height x width: 235x155 mm, Approx. 400 p.
Series: Texts in Computer Science
Pub. Date: 13-Jan-2026
ISBN-13: 9783032063922
Computational geometry plays a vital role in fields ranging from algorithms, data structures, robotics, and computer graphics to geographic information systems and AI.
Providing a comprehensive toolkit, this core textbook constructs a strong bridge between rigorous geometric theory and practical, real-world implementationsmaking complex concepts accessible and engaging. Uniquely, the volume presents a modern approach to computational geometry through the lens of Python programming. Emphasizing clarity, structure, and visualization, the book introduces core geometric structures and algorithms, supported by detailed illustrations and interactive examples. With its project-based learning orientation and emphasis on conceptual understanding, it can serve as both a textbook and a reference guide for those exploring the computational side of geometry.
Core Structures and Algorithms.- Geometric Objects in Python.-
Algorithms for Geometric Objects.- Convex Hull Algorithms.- Polygon
Triangulation Methods.- Delaunay Triangulation.- Voronoi Diagrams.-
Visualization Techniques.- Algorithms for Space Exploration.- Quadtrees.-
Robot Motion Planning.- AI in Computational Geometry.
Format: Hardback, 213 pages, height x width: 235x155 mm, 197 Illustrations, color; 22 Illustrations, black and white
Pub. Date: 21-Dec-2025
ISBN-13: 9783032100870
Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us. From the motion of celestial bodies to the flow of electric currents, ODEs provide the language to describe dynamic systems.
To truly grasp the concepts and techniques of differential equations, practice is paramount. "A Problem-Solving Approach to Ordinary Differential Equations" is your essential guide, offering a comprehensive, four-volume set filled with plenty of meticulously solved, step-by-step problems designed to build your skills and deepen your understanding. This book empowers you to confidently tackle any ODE, transforming challenges into triumphs.
A Review of Limits, Derivatives, and Integrals.- Review of
Trigonometry.- A Review of Algebra.- Classification of Differential
Equations.- First Order Differential Equations.- Solving Differential
Equations with a Change of Variable (I).- Solving Differential Equations with
a Change of Variable (II).- Supplementary Techniques for Solving First-order
Differential Equations.- The Exact Differential Equations.- The Integrating
Factor.- Cauchy-Eulers Equation.- Bernoulli's Equation.- Clairauts
Equation.- Riccatis Equation.
Format: Hardback, 293 pages, height x width: 235x155 mm, 35 Illustrations, color; 18 Illustrations, black and white
Series: Pathways in Mathematics
Pub. Date: 18-Jan-2026
ISBN-13: 9783032106728
This book provides a concise and effective introduction to twisted RabinowitzFloer homology, a generalization of RabinowitzFloer homology. The theory can be used for finding periodic orbits in Hamiltonian systems: applications include results in celestial mechanics and space mission design.
Written in a style that encourages active reflection and trains problem-solving abilities, the book offers a pathway for aspiring researchers from classical mechanics formulated in the language of symplectic geometry to current research in RabinowitzFloer homology and neighboring areas. The book features plenty of examples and exercises, including solutions to most of them, as well as open questions and further directions for research.
Chapter 1. Introduction.- Part I. Classical Mechanics.
Chapter 2. The Hamiltonian Formalism.
Chapter 3. The Lagrangian Formalism.
Chapter 4. The Limit Set of a Family of Periodic Orbits.- Part II. Hamiltonian Floer Homology.
Chapter 5. MorseBott Homology.
Chapter 6. Bubbling Analysis.- Part III. Twisted RabinowitzFloer Homology.
Chapter 7. Definition of Twisted RabinowitzFloer Homology.
Chapter 8. Applications of Twisted RabinowitzFloer Homology.
Chapter 9. Systolic Geometry.
Format: Hardback, 855 pages, height x width: 235x155 mm, 33 Illustrations, color; 2 Illustrations, black and white
Series: Static & Dynamic Game Theory: Foundations & Applications
Pub. Date: 09-Jan-2026
ISBN-13: 9783032070265
Mean-Field-Type Game Theory I is the first of two volumes that together form a comprehensive treatment of mean-field-type game theory and applications, focused on finding state-of-the-art solutions to issues surrounding the next generation of cloud social networking, smart energy systems, transportation and wireless networks. The text shows how mean-field-type game theory provides the ideal framework for designing robust, accurate and efficient algorithms for the autonomous and distributed architectures on which future cities and networks will rely to improve the efficiency and flexibility, security and quality of life.
This first volume enables readers to develop a solid understanding of mean-field-type game theory. It covers key theoretical results such as the stochastic maximum principle and dynamic programming in both discrete and continuous time. The book also covers a wide range of techniques for modeling, designing and analyzing risk and uncertainties using game theory, as well as state-of-the-art distributed mean-field learning algorithm techniques.
Mean-Field-Type Game Theory I: Foundations and New Directions is an ideal resource for academic researchers, and advanced undergraduate and graduate students, surveying basic ideas and advanced topics.
Part 1. Discrete State Markov Games of Mean-Field Type.
Chapter 1. One-Shot Mean-Field-Type Games.
Chapter 2. Markov Games.
Chapter 3. Mean-Field-Type Games with Discrete State Spaces.-
Part 2. Equilibrium Principles.
Chapter 4. Stochastic Maximum Principle.
Chapter 5. Dynamic Programming Principle.-
Part 3. Classes of Mean-Field-Type Games
.
Chapter 6. Non Asymptotic Mean-Field-Type Games.
Chapter 7. Linear-Quadratic Mean-Field and Mean-Field-Type Differential Games.
Chapter 8. Mean-Field-Type Games with Jump and Regime Switching.
Chapter 9. MASS: Master Adjoint Systems.
Chapter 10. Semi-Explicit Solutions in Non-Quadratic Mean-Field-Type Games.
Chapter 11. Stackelberg Mean-Field-Type Games.-
Chapter 12. Mean-Field-Type Games Driven by Rosenblatt Noises.
Chapter 13. Mean-Field-Type Games with Asymmetric Information.
Chapter 14. Difference Games of Mean-Field Type.-
Part 4. Wrap-up.
Chapter 15. Conclusions and New Directions.
Format: Hardback, 89 pages, height x width: 235x155 mm, 10 Illustrations, color
Series: Industrial and Applied Mathematics
Pub. Date: 10-Jan-2026
ISBN-13: 9789819528011
This monograph presents the method of generalized functions and the method of boundary integral equations for solving nonstationary and stationary boundary value problems for classical hyperbolic equations of mathematical physics and electrodynamics: the wave equation, the KleinGordon equation, the Schrödinger equation and the system of Maxwell equations in spaces of dimension 1, 2, 3. It also discusses the theory of generalized functions for solving hyperbolic equations and systems described by pseudo-differential operators. The monograph studies the processes of shock waves, which is often simply impossible within the framework of the classical theory of differential equations. Generalized solutions of the considered boundary value problems, their regular integral representations and resolving singular boundary integral equations have been constructed, which belong to a new class of boundary integral equations, which can become the subject of a separate study in the field of functional analysis and function theory.
Basic Concepts of Generalized Functions Theory: Fundamental Solutions
and their Properties.- Integral Equations of Boundary Value Problems for
SchrodingerGordonFock Equation: Scattering Amplitude.- Nonstationary
Boundary Value Problems for dAlembert Wave Equation and their Solutions.-
Boundary Integral Equations of Nonstationary Boundary Value Problems for the
KleinGordonFock Equation.- Generalized Solutions of Transport Boundary
Value Problems for Wave Equation.- Fundamental and Generalized Solutions of
Maxwell Equations and their Properties.- Generalized Solutions of Stationary
Boundary Value Problems for Maxwell Equations.- Generalized Solutions of
Nonstationary Boundary Value Problems for Maxwell Equations.
Format: Hardback, 265 pages, height x width: 235x155 mm, XVI, 265 p.
Series: Springer Asia Pacific Mathematics Series
Pub. Date: 05-Feb-2026
ISBN-13: 9789819521081
This book provides a systematic summary and condensation of research on infinite-dimensional Hamiltonian operator spectrum theory over the past thirty years, and offers simple and concise proofs for some new achievements.
The book first introduces Hamiltonian systems, both finite-dimensional and infinite-dimensional, laying the foundation for the subsequent introduction of infinite-dimensional Hamiltonian operator spectrum theory. Chapter 2 presents the infinite-dimensional Hamiltonian operator and systematically elaborates on its spectral properties. Chapters 3 and 4 focus on the completeness of the characteristic function system and the symplectic self-adjointness of infinite-dimensional Hamiltonian operators, respectively, achieving improvements and deepening of the relevant content. Chapters 5 and 6 introduce the numerical range and the theory of indefinite metric spaces related to infinite-dimensional Hamiltonian operators, reflecting the broader application prospects of such operators and the novelty of the book's scope.
This book will be useful for senior undergraduate students, graduate students, and teachers specializing in mathematics. To read this book, readers are expected to have knowledge of mathematical analysis and advanced algebra, including matrix theory and some basic knowledge of operator theory.
1. Hamiltonian Systems.-
1.1 Finite-dimensional Hamiltonian Systems and Hamiltonian Matrices.-
1.2 Linear Infinite-dimensional Hamiltonian Canonical Systems and Infinite-dimensional Hamiltonian Operators.-
1.3 Hamiltonian Canonical Systems and the Pseudo-division Algorithm of Multivariate Polynomial Matrices.-
1.4 Monic Factorization of Bivariate Polynomial Matrices.-
1.5 Matrix Method of Solving Characteristic Sequences of the System of Polynomials.-
2 Spectra of Infinite-dimensional Hamiltonian Operators.-
2.1 Spectra of Linear Operators.-
2.2 Spectra of Diagonal Infinite-dimensional Hamiltonian Operators.-
2.3 Spectra of Skew-diagonal Infinite-dimensional Hamiltonian Operators.-
2.4 Spectra of Upper Triangular Infinite-dimensional Hamiltonian Operators.-
2.5 Spectra of Non-negative Hamiltonian Operators.-
2.6 Spectra of the General Infinite-dimensional Hamiltonian Operators.-
3 Completeness of Eigenvector System of Infinite-dimensional Hamiltonian Operators.-
3.1 Infinite-dimensional Symplectic Spaces.-
3.2 Symplectic Orthogonality of Eigenvector System of Infinite-dimensional Hamiltonian Operators.-
3.3 Completeness of Eigenfunction System of 2×2 Infinite-dimensional Hamiltonian Operators.-
3.4 Completeness of the Eigenfunction System of 4×4 Infinite-dimensional Hamiltonian Operators.-
4 Symplectic Self-adjointness of Infinite-dimensional Hamiltonian Operators.-
4.1 Definition of Symplectic Self-adjoint Operators.-
4.2 The Adjoint of the Sum of Two Operators.-
4.3 The Adjoint of Product of Operators.-
4.4 Characterization of Symplectic Self-adjointness by Using the Spectral Set of Infinite-dimensional Hamiltonian Operators.-
5 Numerical Range Theory of Infinite-dimensional Hamiltonian Operators.-
5.1 Numerical Range and Its Definition.-
5.2 Numerical Range of Infinite-dimensional Hamiltonian Operators.-
5.3 Numerical Radius of Infinite-dimensional Hamiltonian Operators.-
5.4 Quadratic Numerical Range of Infinite-dimensional Hamiltonian Operators.-
5.5 Quadratic Numerical Radius of Infinite-dimensional Hamiltonian Operator.-
5.6 Essential Numerical Range of Infinite-dimensional Hamiltonian Operators.-
6 Spectral Theory of Infinite-dimensional Hamiltonian Operators in Complete Indefinite Inner Product Spaces.-
6.1 Krein Spaces.-
6.2 Spectra of Infinite-dimensional Hamiltonian Operators in Krein Spaces.-
6.3 numerical Range in Krein Spaces.
Format: Hardback, 284 pages, height x width: 235x155 mm, 5 Illustrations, black and white
Series: Springer Monographs in Mathematics
Pub. Date: 15-Dec-2025
ISBN-13: 9783032103772
The objects of concern in this book are the sheaf-cohomology groups of locally symmetric spaces attached to arithmetically defined groups G, contained in an algebraic group. The sheaves are associated to G-modules over the ring of integers or finite extension rings thereof. There is an action of a Hecke algebra on these cohomology groups. Accordingly, they decompose into indecomposable pieces which are of great interest in number theory and algebraic geometry. Upon extending the coefficient systems to complex vector spaces, an individual indecomposable component corresponds to a space of automorphic forms, thereby, giving rise to an attached L-function. For example, the Ramanujan Delta function provides the first case of such a correspondence. Up to division by a carefully chosen period, these L-functions take rational (algebraic) values at certain critical arguments. In various examples, it is discussed how the numerator and denominator ideals of these normalised values shed some light on the integral structure of the cohomology groups as a module under the Hecke algebra. In particular, results concern the denominator of cohomology classes which are represented by Eisenstein series, analytically constructed beforehand. In very special cases, values of the Riemann zeta-function play a decisive role. Within the discussion of these number-theoretic aspects of the cohomology groups, questions of a computational nature unfold. These may lead, by means of experiments, to a better understanding of the general integral structure of these groups. This introduction to the cohomology of arithmetic groups and the associated theory of automorphic forms and special values of L-functions focuses on number theoretic aspects and questions. It is intended for graduate students and researchers in the field of arithmetic as well as in automorphic forms and differential geometry.
1 Basic Notions and Definitions.- 2 The Cohomology Groups.- 3 Hecke Operators.- 4 Representation Theory.- 5 Applications to Number Theory.- 6 Analytic Methods.
Format: Paperback / softback, 116 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Series: SpringerBriefs in Statistics
Pub. Date: 08-Jan-2026
ISBN-13: 9783032089236
The primary purpose of this book is to introduce the reader to elementary statistical methods as related to tests of differences, such as one-sample tests, tests of two independent samples, tests of two matched samples, and one-way analysis of variance. Throughout the book the emphasis is on permutation statistical methods, although the results of the permutation analyses are always compared and contrasted with the results of conventional statistical analyses. Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity, depend only on the observed data, and do not require random sampling. The book is designed for an audience with limited statistical background and can easily serve as a supplementary textbook in an undergraduate or graduate course in departments such as statistics, psychology, economics, or biology. In particular, the audience for this book is quantitative undergraduate and graduate students in fields such as psychology, sociology, biology and political science. No statistical training beyond a first course in statistics is required.
1. Introduction.-
2. Permutation Methods.-
3.Analysis of One-Sample Data.-
4.Analysis of Two-Sample Data.-
5.Analysis of Matched-Pairs Data.-
6.Analysis of Multi-Sample Data.-
Reference.- Author Index.- Subject Index.