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Ordinary Differential Equations and
Special Functions

Ordinary Differential Equations and Special Functions

De Gruyter Series in Nonlinear Analysis and Applications

Dynamics, Coexistence and Persistence

Cross-Diffusion Systems

Differential and Difference Equations with Applications in Queueing Theory

Boundary Value Problems and Partial Differential Equations

Essays in Developmental Psychology

Perspectives from Developmental Psychology

Attitudes and Emotions Towards Mathematics

Storytelling with Data Box Set

Series on Advances in Mathematics for Applied Sciences

This monograph presents an integral method for analysing the dynamic behaviour of nonlinear, nonstationary, and controlled systems. The method is based on the use of nonlinear integral inequalities to obtain new estimates for the norms of solutions and Lyapunov functions for the corresponding systems of differential equations of disturbed motion.The book consists of seven chapters. The first chapter establishes new bounds for solutions to ordinary and infinite systems of differential equations using nonlinear integral inequalities in pseudo-linear form. The second chapter studies the equations of disturbed motion based on new estimates of Lyapunov functions. Here, conditions are established for various types of motion boundedness, including the stability of coupled systems under initial and subsequent disturbances. The third chapter is devoted to polynomial systems, where variations of Lyapunov functions are used to derive conditions for stability and stabilisation of motion, including the analysis of the zero solution of systems with aftereffects.Chapter 4 applies nonlinear integral inequalities to nonlinear systems with interval initial conditions, and studies the stabilisation of systems with multiple controls. Chapter 5 focuses on quasilinear systems with fractional derivatives, establishing conditions for boundedness and Lagrange stability. Chapter 6 introduces an integral method for time-scale dynamic equations with fractional derivatives, offering new tools for stability and boundedness analysis. The final chapter studies equilibrium stability in a model of confrontation between two countries and alliances, using Lyapunov functions and integral inequalities to determine conditions for stable equilibrium and changes in weapon levels.

Integral Methods In Nonlinear Dynamics Of Systems

Tauche ein in die Elektrodynamik mit einem Lehrbuch, welches die Maxwellschen Gleichungen als Ausgangspunkt nutzt, wodurch Schritt für Schritt ein tiefes Verständnis vermittelt wird.&nbsp;Besonderheiten:Dieses Buch beginnt jedes Kapitel mit einer der Maxwellschen Gleichungen und erklärt dann schrittweise die einzelnen Bestandteile.&nbsp;Anfänger/innen haben so ein konkretes Lernziel vor Augen.&nbsp;Sowohl die vorkommenden physikalischen Größen als auch mathematischen Grundlagen werden in ihrem natürlichen Kontext erklärt. Grundlegende Prinzipien und komplexe Konzepte werden für verschiedene Fälle betrachtet und mit einfachen Beispielen verdeutlicht. Mithilfe von Aufgaben und Lösungen – sowohl klassisch im Buch als auch als digitale Karteikarten für unterwegs – kann das erworbene Wissen eingeübt und vertieft werden.&nbsp;Inhalt:1. Das Gaußsche Gesetz für elektrische Felder – 2. Das Gaußsche Gesetz für magnetische Felder –&nbsp;3. Das Faradaysche Induktionsgesetz&nbsp;– 4. Das Ampère-Maxwellsche Gesetz – 5. Weiterführende Themen der Elektrodynamik – 6. Wechselwirkung von elektrischen und magnetischen Feldern mit Materie&nbsp;Zielgruppe:Studierende der Ingenieurwissenschaften und Naturwissenschaften, wie z.B. Elektrotechnik, Physik, Medizinphysik, etc. als auch Interessierte bzw. Berufstätige, die ein tieferes Verständnis für die Grundlagen der Elektrodynamik entwickeln möchten.&nbsp;Vorkenntnisse: Hilfreich sind physikalische Grundkenntnisse wie sie z.B. im Buch Vorkurs Physik fürs MINT-Studium vermittelt werden.&nbsp;Der Autor:Dr. Patrick Steglich&nbsp;promovierte 2017 an der Universität Rom ‚Tor Vergata‘ und habilitierte 2023 an der Brandenburgischen Technischen Universität Cottbus-Senftenberg.&nbsp;Seit 2018 ist er Dozent mit Lehrauftrag an der Technischen Hochschule Wildau&nbsp;für das Fach Elektrodynamik und forscht am Leibniz-Institut für innovative Mikroelektronik.

Eine schrittweise Reise durch Maxwells Gleichungen

Klassische Elektrodynamik

Mathematics Study Resources

What kind of objects does mathematics investigate, and in what sense do these objects exist? Why are we justified in considering mathematical statements as part of our knowledge, and how can they be validated? A philosophy of mathematics seeks to answer such questions. In this introduction, we present the major positions in the philosophy of mathematics and formulate their core ideas into clear, accessible theses. Readers will learn which philosophers developed each position and the historical context in which they emerged. Drawing on fundamental intuitions and scientific findings, one can argue for or against these theses – such arguments form the second focus of this book. The book aims to encourage readers to reflect on the philosophy of mathematics, to develop their own stance, and to learn how to argue for it.
This book is a translation of the original German 2nd edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.
The Author
Jörg Neunhäuserer earned his doctorate in mathematics at Freie Universität Berlin. He has published numerous articles in academic journals and has taught mathematics lectures in various bachelor's and master's programs at the universities of Berlin, Brunswick, Clausthal, Dresden, Hanover, Göttingen and Lüneburg. His German-language books on Mathematical Concepts and Beautiful Theorems of Mathematics are also available from Springer Spektrum.

Introduction to the Philosophy of Mathematics

Enables readers to learn how to design and implement algorithms for efficient and secure smart technologies Algorithms for Smart World Technologies explains the fundamentals of key algorithms and their application in a variety of use cases, covering the factors, assumptions, and models essential for the design of a real-world algorithm and discussing the importance of advanced algorithms in the use of modern world technologies such as AI, IoT, and Blockchain. Each chapter is written to provide a self-contained treatment of one major topic. Collectively, the chapters have been designed and carefully integrated to be entirely complementary with respect to definitions, terminology, and notation. Chapters are divided into three parts-complexities, paradigms, and recent applications-and at the beginning of each part, a detailed introduction explaining each subject area is provided. The foundational subjects are supported by end-of-chapter exercises and case studies, while the application-focused chapters are supported by projects to give worked experience. Written by two highly qualified authors in academia, sample topics covered in Algorithms for Smart World Technologies include: Complexities, including complex systems and algorithms, measuring efficiency, types of systems, and types of complexities Ethics bounds, including algorithms ethics maps, algorithmic traceability, social ethics, environmental ethics, and parameters and thresholdsAlgorithmic paradigms, including the design of an algorithm, the divide and conquer algorithm, backtracking, exhaustive search, solvability, and reducibilityIntelligent search algorithms, including solution space, uninformed, and informed search algorithms, evolutionary algorithms, and nature-inspired algorithmsSmart transportation, including scheduling algorithms for vehicular traffic and opportunistic communication for VANETWritten for developers and domain experts who want to explore the opportunities and challenges of designing and developing algorithms and protocols for Smart-world problems, Algorithms for Smart World Technologies is an authoritative resource on the topic that provides both foundational knowledge and guidance on practical applications.

A Comprehensive Guide to Applications in AI, IoT and Automation for Electrical and Computer Engineers

Algorithms for Smart World Technologies

Series On Analysis, Applications And Computation

The book is devoted to rigorous mathematical results on discrete nonlinear Schrödinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations emerge as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there is necessary material from the spectral theory of discrete Schrödinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.

Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability

Smart Thinking

A new smart-thinking series that applies complex mathematical ideas to everyday scenarios.

Mathematical answers to life’s key questions

Why Don’t Rabbits Rule The World?

The Science of Scaling Revenue

Ordinary Differential Equations and Special Functions

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