Textbook
Mar 2026
With this book, understanding comes naturally through doing
All topics of mathematics, which users in the first semester really need
Digestible bites: Each chapter is for a double-hour lecture
This book provides a clear and easy-to-understand introduction to higher mathematics with numerous examples. The author shows how to solve typical problems in a recipe-like manner and divides the material into short, easily digestible learning units.
Have you ever cooked a 3-course meal based on a recipe? That generally works quite well, even if you are not a great cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise: Need to solve a Riccati's differential equation or the singular value decomposition of a matrix? Look it up in this book, you'll find a recipe for it here. Recipes are available for problems from the field of:
· Calculus in one and more variables,
· Linear algebra,
· Vector analysis,
· Theory on differential equations, ordinary and partial,
· Theory of integral transformations,
· Function theory.
Other features of this book include:
· The division of Higher Mathematics into approximately 100 chapters of roughly equal length. Each chapter covers approximately the material of a 90-minute lecture.
· Numerous exercises and solutions
· Many problems in higher mathematics can be solved with computers. We always indicate how it works with MATLAB®.
This 2nd English edition has been completely revised and numerous examples, illustrations, explanations and further exercises have been added.
Book
Mar 2026
Overview
Offer a fresh measurable perspective on topological dynamics, bridging classical theory with modern insights
Translate classical topological results into measurable terms to provide new interpretations and applications
Guide young researchers toward a unified approach to measure-preserving and topological dynamical systems
Part of the book series: Springer Asia Pacific Mathematics Series (SAPACM, volume 14)
About this book
This book introduces a new measurable perspective on dynamical systems by connecting concepts from topological dynamics with their measure-theoretic counterparts. A central theme is the translation of topological notions into measurable ones. For example, minimality in topological dynamics suggests a measurable analogue in ergodicity, where every invariant measurable set has either zero or full measure, offering an intuitive parallel between the two settings. Likewise, the notion of expansiveness is reinterpreted through expansive measures, in which almost all orbits separate beyond a fixed radius. These measurable analogues extend naturally to homeomorphisms and flows on compact metric spaces, which are explored in depth in Chapters 3 and 7.
Building on this framework, the book develops measurable versions of several structural results from topological dynamics. Walters’ stability theorem-grounded in shadowing, expansiveness, and topological stability-is revisited in Chapters 4 and 8 from a measurable perspective, while Smale’s spectral decomposition theorem is reformulated in measurable terms in Chapters 5 and 9. By bridging topological and measurable viewpoints, the book offers a cohesive approach that provides new insights and directions for the study of dynamical systems.
Textbook
Mar 2026
Offers an in-depth visual approach to multivariable and vector calculus
Complements existing textbooks on the subject by being concise and portable
Includes over one hundred carefully drawn figures that illustrate the material with clarity and ingenuity
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With nearly 200 carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. The text will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
The second edition has been extensively revised. Several sections in the chapters on vectors and functions, differentiation of multivariable functions, and vector calculus have been completely rewritten. Other portions of the first edition have been reorganized, with some material relocated to more suitable sections. Many discussions have been expanded, and explanatory passages have been refined for greater clarity. A significant amount of new material has been added, primarily to provide a more comprehensive treatment of specific topics. Some original exercises have been replaced with fully worked examples, offering a more balanced guide for the reader. In addition, seventy new supplementary problems have been included, and asterisks now identify the more challenging ones.
Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques.
Conference proceedings
Mar 2026
Highlights different approaches to analysing the biological process of chemotaxis
Encompasses a wide range of different techniques applied in different mathematical approaches
Presents novel models that capture realistic effects not covered in classical models
Part of the book series: SEMA SIMAI Springer Series (SEMA SIMAI, volume 43)
This book provides the latest scientific advances presented at the 9ECM for mathematical modeling of the biological process of chemotaxis. The wide range of techniques presented includes seven contributions from various countries, approaches exploring different properties and numerical approaches. Taxis is an important biological process that takes place in embryonic development, cancer invasion and tumor angiogenesis, among others. In fact, it is present in everything that induces movement in living organisms. More specifically, in chemotaxis, movement is induced by a chemical agent. Mathematical models of chemotaxis, since the pioneering work of Keller and Segel, attempt to reproduce this biological process. In addition to the advantages that mathematical models can have for optimizing resources and improving treatments associated with living organisms, their study from a theoretical and numerical perspective raises a mathematical challenge. The target audience of this book is any researcher interested in the mathematical analysis of biological phenomena associated with any type of taxis and modeled with PDEs.
Book
Mar 2026
Provides a timely overview of applications of classical Lie theory as well as its recent developments
Offers a self-contained approach by explaining the theoretical arguments on which the applications are built
Describes and directs readers to two open source algebra packages designed to help manage these complex computations
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 55)
Part of the book sub series: Advances in Continuum Mechanics (ACM)
This monograph provides a timely overview of recent developments in classical Lie theory as well as concrete examples in applied mathematics and mathematical physics. Utilizing a comprehensive and self-contained approach, the author provides clear explanations of the theoretical arguments on which the applications are built. Specific examples with physical applications include the cylindrical Korteweg–de Vries equations, the Navier-Stokes-Fourier equations, the three-body problem, and more. With the author's focus on the utility and algorithmic nature of Lie group analysis of differential equations, readers will gain a deeper understanding of the mathematics underpinning these applications. The author also describes and directs readers to two open source algebra packages designed to help manage these complex computations.
Lie Symmetries of Differential Equations will appeal to researchers in applied mathematics, particularly those in mathematical physics interested in exploring Lie group analysis.
Textbook
Mar 2026
Clearly explains all central topics and concepts in an illustrative and memorable way
Separates algebraic from analytical methods, making it easier to get started
Includes many examples from various application areas as well as supplementary Python code
Access Source Code
Part of the book series: Mathematics Study Resources (MSR, volume 25)
This textbook presents the theoretical foundations of numerical mathematics in a modern, application-oriented, and comprehensive way. In addition to the standard content, it includes numerous examples and practical excursions to sustainably enhance understanding. Proofs are presented in a very detailed, step-by-step manner. The recurring core concepts of numerical mathematics like accuracy, efficiency, robustness and stability are explicitly addressed and clearly distinguished from one another. Specific example calculations for the described algorithms are carried out using provided Python codes. Numerical modeling for aspects of machine learning and neural networks are taken into consideration. Furthermore, numerical methods from linear algebra and analysis are presented separately, which significantly facilitates students’ access to numerical mathematics – based on the two main lectures within undergraduate studies in mathematics. Therefore, the book is ideally suited for students of mathematics, physics, computer science, or engineering.
This book is a translation of the original German 2nd edition of “Einführung in die Numerische Mathematik” (Springer, 2024). The translation was done with the help of artificial intelligence. A subsequent revision was performed by the authors to further refine the work and to ensure that the translation is appropriate concerning content and scientific correctness.
Textbook
Mar 2026
Covers a wide range of topics, including many not covered in other textbooks
Includes chapters on special functions, complex ODEs, and complex dynamics
Has plenty of exercises, some with solutions
This elegant textbook offers a comprehensive course on one-dimensional complex analysis. It includes many topics that, in this scope, are not covered in most other textbooks, such as a detailed investigation of the Schwarzian derivative and its associated differential equation, with applications to conformal mappings of circular polygons; various proofs of the uniformisation theorem for planar domains; an introduction to the theory of ordinary differential equations in the complex domain, culminating in a proof of the Cauchy–Kovalevskaya theorem; an introduction to the theory of normal families, including Zalcman's lemma; a proof of the Paley–Wiener theorem; a complete discussion of the Laguerre–Pólya class; solution of the Dirichlet problem, with special emphasis on harmonic measure and Green's function, and applications to conformal mappings of multiply connected domains; a detailed description of the dynamics of polynomials; and the consistent use of the theory of proper mappings whenever possible.
Book
Mar 2026
Provides a comprehensive study of various fixed-point theorems, such as in metric, b-metric and partial metric spaces
Addresses the need for rigorous analytical methods in optimization, computational mathematics and applied sciences
Discusses applications in traffic systems, stock market analysis, iterative algorithms and differential equations
Part of the book series: Industrial and Applied Mathematics (INAMA)
This contributed volume contains chapters on various fixed-point theorems, including those in metric, b-metric and partial metric spaces. The book addresses the need for rigorous analytical methods in optimization, computational mathematics and applied sciences. By offering innovative solutions through iterative schemes and contraction principles, it bridges the gap between abstract mathematical principles and practical problem-solving approaches. The concept of fixed points has deep mathematical significance, influencing both theoretical frameworks and real-world applications. The book highlights the applications of fixed-point theory, presenting fundamental concepts and modern advancements, in diverse fields such as traffic control systems, stock market analysis, iterative algorithms and differential equations.
Textbook
Mar 2026
Presents essential knowledge in a compact format
Concentrates on the theoretical fundamentals relevant to applied mathematics
Includes carefully chosen examples and exercises
Part of the book series: Compact Textbooks in Mathematics (CTM)
Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing.
This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.
In this second edition, corrections and improvements have been made. In addition, study review questions have been added to each chapter, providing readers with a tool for self-assessment.