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Fundamentals of Ramsey Theory (Discrete Mathematics and Its Applications)
by Aaron RobertsonRamsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before. The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises. This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTS Preface List of Figures List of Tables Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography Index Biography Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
Fundamentals of Real and Complex Analysis (Springer Undergraduate Mathematics Series)
by Asuman Güven AksoyThe primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science.Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter’s unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy’s theorem through the integral formula and residue theorem are presented.
Fundamentals of Scientific Computing
by Bertil GustafssonThe book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today's weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models - sets of equations - that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.
Fundamentals of Scientific Mathematics (Dover Books on Mathematics)
by George E. OwenThis rewarding text, beautifully illustrated by the author and written with superb clarity, offers undergraduate students a solid mathematical background and functions equally well for independent study.The five-part treatment begins with geometry, defining three-dimensional Euclidean space and its axioms, the coordinate system and coordinate transformation, and matrices. A review of vector algebra covers vector properties, multiplication, the resolution of a vector along a complete set of base vectors, and vector transformations. Topics in analytic geometry introduce loci, straight lines, the plane, two-dimensional curves, and the quadratic form. Functions are defined, as are intervals, along with multiplicity, the slope at a point, continuity, and areas. The concluding chapter, on differential and integral calculus, explains the concept of a limit, the derivative, the integral, differential equations, and applications of the calculus to kinematics.
Fundamentals of Signal Processing in Metric Spaces with Lattice Properties: Algebraic Approach
by Andrey PopoffExploring the interrelation between information theory and signal processing theory, the book contains a new algebraic approach to signal processing theory. Readers will learn this new approach to constructing the unified mathematical fundamentals of both information theory and signal processing theory in addition to new methods of evaluating quality indices of signal processing. The book discusses the methodology of synthesis and analysis of signal processing algorithms providing qualitative increase of signal processing efficiency under parametric and nonparametric prior uncertainty conditions. Examples are included throughout the book to further emphasize new material.
Fundamentals of Single Cavitation Bubble Dynamics (SpringerBriefs in Energy)
by Xiaoyu Wang Yuning Zhang Qi Liang Yufei WangThis brief provides a comprehensive review of the rapidly expanding field of cavitation and bubble dynamics, covering the discussion of bubble dynamics equations, bubble oscillation dynamics, theoretical prediction models of jets, and high-speed photography technology. Among them, the core formulas, important research methods, and typical results related to bubble oscillation and collapse dynamics are systematically and comprehensively introduced. Specifically, in terms of the bubble dynamics equations, several classical dynamic equations utilized to describe the radial motion of the spherical bubble, cylindrical bubble, and the bubble in a droplet are derived and compared. In terms of the bubble oscillation dynamics, based on the perturbation method, multi-scale method, and Laplace transform method, the nonlinear oscillation characteristics of the bubble in free oscillation and driven oscillation are analyzed. In terms of the jet prediction theory, the Kelvin impulse model and various boundary treatment methods are given in detail, and the jet direction, intensity, and spatial sensitivity caused by the bubble collapse near various boundaries are discussed. In terms of the bubble collapse visualization based on the high-speed photography, taking the laser-induced bubble as an example, the system composition, operation process and experimental layout of the high-speed photography experimental platform are introduced, and a large number of typical bubble collapse deformation, jet evolution and shock wave propagation characteristics obtained from experiments are demonstrated. This book is intended for academic researchers and graduate students in fluid dynamics, aiming to consolidate the basic theory, physical mechanism, and latest progress in the field of bubble dynamics.
Fundamentals of Spherical Array Processing
by Boaz RafaelyThis book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. The third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters present various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, including beamformers that achieve maximum directivity and maximum robustness, and the Dolph-Chebyshev beamformer are developed. The final chapter discusses more advanced beamformers, such as MVDR and LCMV, which are tailored to the measured sound field.
Fundamentals of Spherical Array Processing (Springer Topics In Signal Processing Ser. #8)
by Boaz RafaelyThis book provides a comprehensive introduction to the theory and practice of spherical microphone arrays, and was written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. The new edition includes additions and modifications, and references supplementary Matlab code to provide the reader with a straightforward start for own implementations. The book is also accompanied by a Matlab manual, which explains how to implement the examples and simulations presented in the book.The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. In turn, the third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters highlight various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, including those that achieve maximum directivity and maximum robustness are developed, along with the Dolph–Chebyshev beamformer. The final chapter discusses more advanced beamformers, such as MVDR (minimum variance distortionless response) and LCMV (linearly constrained minimum variance) types, which are tailored to the measured sound field.
Fundamentals of Statistical Experimental Design and Analysis
by Robert G. EasterlingProfessionals in all areas - business; government; the physical, life, and social sciences; engineering; medicine, etc. - benefit from using statistical experimental design to better understand their worlds and then use that understanding to improve the products, processes, and programs they are responsible for. This book aims to provide the practitioners of tomorrow with a memorable, easy to read, engaging guide to statistics and experimental design. This book uses examples, drawn from a variety of established texts, and embeds them in a business or scientific context, seasoned with a dash of humor, to emphasize the issues and ideas that led to the experiment and the what-do-we-do-next? steps after the experiment. Graphical data displays are emphasized as means of discovery and communication and formulas are minimized, with a focus on interpreting the results that software produce. The role of subject-matter knowledge, and passion, is also illustrated. The examples do not require specialized knowledge, and the lessons they contain are transferrable to other contexts. Fundamentals of Statistical Experimental Design and Analysis introduces the basic elements of an experimental design, and the basic concepts underlying statistical analyses. Subsequent chapters address the following families of experimental designs: Completely Randomized designs, with single or multiple treatment factors, quantitative or qualitative Randomized Block designs Latin Square designs Split-Unit designs Repeated Measures designs Robust designs Optimal designs Written in an accessible, student-friendly style, this book is suitable for a general audience and particularly for those professionals seeking to improve and apply their understanding of experimental design.
Fundamentals of Statistical Inference: What is the Meaning of Random Error? (SpringerBriefs in Applied Statistics and Econometrics)
by Norbert Hirschauer Sven Grüner Oliver MußhoffThis book provides a coherent description of foundational matters concerning statistical inference and shows how statistics can help us make inductive inferences about a broader context, based only on a limited dataset such as a random sample drawn from a larger population. By relating those basics to the methodological debate about inferential errors associated with p-values and statistical significance testing, readers are provided with a clear grasp of what statistical inference presupposes, and what it can and cannot do. To facilitate intuition, the representations throughout the book are as non-technical as possible.The central inspiration behind the text comes from the scientific debate about good statistical practices and the replication crisis. Calls for statistical reform include an unprecedented methodological warning from the American Statistical Association in 2016, a special issue “Statistical Inference in the 21st Century: A World Beyond p The American Statistician in 2019, and a widely supported call to “Retire statistical significance” in Nature in 2019.The book elucidates the probabilistic foundations and the potential of sample-based inferences, including random data generation, effect size estimation, and the assessment of estimation uncertainty caused by random error. Based on a thorough understanding of those basics, it then describes the p-value concept and the null-hypothesis-significance-testing ritual, and finally points out the ensuing inferential errors. This provides readers with the competence to avoid ill-guided statistical routines and misinterpretations of statistical quantities in the future.Intended for readers with an interest in understanding the role of statistical inference, the book provides a prudent assessment of the knowledge gain that can be obtained from a particular set of data under consideration of the uncertainty caused by random error. More particularly, it offers an accessible resource for graduate students as well as statistical practitioners who have a basic knowledge of statistics. Last but not least, it is aimed at scientists with a genuine methodological interest in the above-mentioned reform debate.
Fundamentals of Statistics for Aviation Research (Aviation Fundamentals)
by Michael A. Gallo Brooke E. Wheeler Isaac M. SilverThis is the first textbook designed to teach statistics to students in aviation courses. All examples and exercises are grounded in an aviation context, including flight instruction, air traffic control, airport management, and human factors. Structured in six parts, this book covers the key foundational topics relative to descriptive and inferential statistics, including hypothesis testing, confidence intervals, z and t tests, correlation, regression, ANOVA, and chi-square. In addition, this book promotes both procedural knowledge and conceptual understanding. Detailed, guided examples are presented from the perspective of conducting a research study. Each analysis technique is clearly explained, enabling readers to understand, carry out, and report results correctly. Students are further supported by a range of pedagogical features in each chapter, including objectives, a summary, and a vocabulary check. Digital supplements comprise downloadable data sets and short video lectures explaining key concepts. Instructors also have access to PPT slides and an instructor’s manual that consists of a test bank with multiple choice exams, exercises with data sets, and solutions. This is the ideal statistics textbook for aviation courses globally, especially in aviation statistics, research methods in aviation, human factors, and related areas.
Fundamentals of Statistics in Health Administration
by Robert W. BroylesFundamentals of Statistics in Health Administration fills the needs of both students and practicing health care managers who must apply statistical concepts and methods to real world health care management problems and issues. It covers the fundamentals of statistics in a user-friendly way, with a strong emphasis on practical application in health administration. The text is highly structured with step-by-step instructions throughout. There is an emphasis on Excel and other commonly used programs, although manual calculations are given careful attention as well.
Fundamentals of Stochastic Networks
by Oliver C. IbeAn interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physical sciences. The author uniquely unites different types of stochastic, queueing, and graphical networks that are typically studied independently of each other. With balanced coverage, the book is organized into three succinct parts: Part I introduces basic concepts in probability and stochastic processes, with coverage on counting, Poisson, renewal, and Markov processes Part II addresses basic queueing theory, with a focus on Markovian queueing systems and also explores advanced queueing theory, queueing networks, and approximations of queueing networks Part III focuses on graphical models, presenting an introduction to graph theory along with Bayesian, Boolean, and random networks The author presents the material in a self-contained style that helps readers apply the presented methods and techniques to science and engineering applications. Numerous practical examples are also provided throughout, including all related mathematical details. Featuring basic results without heavy emphasis on proving theorems, Fundamentals of Stochastic Networks is a suitable book for courses on probability and stochastic networks, stochastic network calculus, and stochastic network optimization at the upper-undergraduate and graduate levels. The book also serves as a reference for researchers and network professionals who would like to learn more about the general principles of stochastic networks.
Fundamentals of Structural Engineering
by Jerome J. Connor Susan FarajiFundamentals of Structural Engineering provides a balanced, seamless treatment of both classic, analytic methods and contemporary, computer-based techniques for conceptualizing and designing a structure. The book?s principle goal is to foster an intuitive understanding of structural behavior based on problem solving experience for students of civil engineering and architecture who have been exposed to the basic concepts of engineering mechanics and mechanics of materials. Distinct from many undergraduate textbooks, which are focused mainly on either teaching manual analysis methods and applying them to simple, idealized structures or reformulating structural analysis methods in terms of matrix notation, this text instead encourages the student to develop intuition about structural behavior. The authors of this text recognize the notion that engineers reason about behavior using simple models and intuition they acquire through problem solving. The approach adopted in this text develops this type of intuition by presenting extensive, realistic problems and case studies together with computer simulation, which allows rapid exploration of how a structure responds to changes in geometry and physical parameters.
Fundamentals of Structural Optimization: Shape, Anisotropy, Topology (Mathematical Engineering)
by Vladimir KobelevThis book provides a comprehensive overview of analytical methods for solving optimization problems, covering principles and mathematical techniques alongside numerical solution routines, including MAPLE and MAXIMA optimization routines. Each method is explained with practical applications and ANSYS APDL scripts for select problems. Chapters delve into topics such as scaling methods, torsion compliance, shape variation, topological optimization, anisotropic material properties, and differential geometry. Specific optimization problems, including stress minimization and mass reduction under constraints, are addressed. The book also explores isoperimetric inequalities and optimal material selection principles. Appendices offer insights into tensors, differential geometry, integral equations, and computer algebra codes. Overall, it's a comprehensive guide for engineers and researchers in structural optimization.
Fundamentals of Supervised Machine Learning: With Applications in Python, R, and Stata (Statistics and Computing)
by Giovanni CerulliThis book presents the fundamental theoretical notions of supervised machine learning along with a wide range of applications using Python, R, and Stata. It provides a balance between theory and applications and fosters an understanding and awareness of the availability of machine learning methods over different software platforms.After introducing the machine learning basics, the focus turns to a broad spectrum of topics: model selection and regularization, discriminant analysis, nearest neighbors, support vector machines, tree modeling, artificial neural networks, deep learning, and sentiment analysis. Each chapter is self-contained and comprises an initial theoretical part, where the basics of the methodologies are explained, followed by an applicative part, where the methods are applied to real-world datasets. Numerous examples are included and, for ease of reproducibility, the Python, R, and Stata codes used in the text, along with the related datasets, are available online.The intended audience is PhD students, researchers and practitioners from various disciplines, including economics and other social sciences, medicine and epidemiology, who have a good understanding of basic statistics and a working knowledge of statistical software, and who want to apply machine learning methods in their work.
Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds
by Uwe MühlichThis book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept.After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters.It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
Fundamentals of Time-Dependent Density Functional Theory
by Fernando M.S. Nogueira Miguel A.L. Marques Angel Rubio Neepa T. Maitra E.K.U. GrossThere have been many significant advances in time-dependent density functional theory over recent years, both in enlightening the fundamental theoretical basis of the theory, as well as in computational algorithms and applications. This book, as successor to the highly successful volume Time-Dependent Density Functional Theory (Lect. Notes Phys. 706, 2006) brings together for the first time all recent developments in a systematic and coherent way. First, a thorough pedagogical presentation of the fundamental theory is given, clarifying aspects of the original proofs and theorems, as well as presenting fresh developments that extend the theory into new realms--such as alternative proofs of the original Runge-Gross theorem, open quantum systems, and dispersion forces to name but a few. Next, all of the basic concepts are introduced sequentially and building in complexity, eventually reaching the level of open problems of interest. Contemporary applications of the theory are discussed, from real-time coupled-electron-ion dynamics, to excited-state dynamics and molecular transport. Last but not least, the authors introduce and review recent advances in computational implementation, including massively parallel architectures and graphical processing units. Special care has been taken in editing this volume as a multi-author textbook, following a coherent line of thought, and making all the relevant connections between chapters and concepts consistent throughout. As such it will prove to be the text of reference in this field, both for beginners as well as expert researchers and lecturers teaching advanced quantum mechanical methods to model complex physical systems, from molecules to nanostructures, from biocomplexes to surfaces, solids and liquids. From the reviews of LNP 706: "This is a well structured text, with a common set of notations and a single comprehensive and up-to-date list of references, rather than just a compilation of research articles. Because of its clear organization, the book can be used by novices (basic knowledge of ground-state DFT is assumed) and experienced users of TD-DFT, as well as developers in the field." (Anna I. Krylov, Journal of the American Chemical Society, Vol. 129 (21), 2007) "This book is a treasure of knowledge and I highly recommend it. Although it is a compilation of chapters written by many different leading researchers involved in development and application of TDDFT, the contributors have taken great care to make sure the book is pedagogically sound and the chapters complement each other [...]. It is highly accessible to any graduate student of chemistry or physics with a solid grounding in many-particle quantum mechanics, wishing to understand both the fundamental theory as well as the exponentially growing number of applications. [...] In any case, no matter what your background is, it is a must-read and an excellent reference to have on your shelf." Amazon.com, October 15, 2008, David Tempel (Cambridge, MA)
Fundamentals of Traffic Simulation
by Jaume BarcelóThe increasing power of computer technologies, the evolution of software engineering and the advent of Intelligent Transport Systems (ITS) worldwide has helped make traffic simulation one of the most used approaches for traffic analysis in support of the design and evaluation of traffic systems. The ability of traffic simulation software to emulate the time variability of traffic phenomena makes it a uniquely useful tool for capturing the complexity of traffic systems. While a wide variety of simulation software is available, no one book has presented a unified treatment of the subject. Fundamentals of Traffic Simulation is the first book to provide practitioners and researchers with a comprehensive treatment of the state of the art of traffic simulation. Leading researchers worldwide provide up-to-date information on: Simulation as a well established and grounded OR technique and its specificities when applied to traffic systems The main approaches to traffic simulation and the principles of traffic simulation model building The fundamentals of traffic flow theory and its application to traffic simulation in Microscopic traffic modeling Mesoscopic traffic modeling Macroscopic traffic modeling The principles of Dynamic Traffic Assignment and its application to traffic simulation The calibration and validation of traffic simulation models This important work will appeal to professionals, including transport consultants, managers in design firms and government, and even simulation software developers. It will also provide researchers with the first comprehensive overview of the subject, and can serve as a text or recommended reading in courses on traffic simulation and transportation analysis.
Fundamentals of Wearable Computers and Augmented Reality
by Woodrow BarfieldData will not help you if you can't see it where you need it. Or can't collect it where you need it. Upon these principles, wearable technology was born. And although smart watches and fitness trackers have become almost ubiquitous, with in-body sensors on the horizon, the future applications of wearable computers hold so much more. A trusted refer
Fundamentals of the Insurance Business (Springer Texts in Business and Economics)
by Massimiliano Maggioni Giuseppe TurchettiThis textbook presents the fundamental economic dimensions of insurance companies and links them to managerial issues. Combining academic rigour and a strongly practice-oriented approach, it addresses both the competitive environment and the management of the insurance business. Further, it provides a general overview of insurance undertakings and technical topics are explained in depth. Filling an important gap in the market for textbooks on the insurance business, it is divided into four parts and 35 chapters. Part I (chapters 1 to 10) describes the fundamentals of the business, how the industry works, the Authorities and the regulations. It presents the insurance products (for life, non-life retail, and non-life commercial lines). Part II (chapters 11 to 17) explains the pricing and reserving for life and non-life insurance. Reinsurance business is also illustrated. Part III (chapters 18 to 25) describes business models in the industry and the organizational structures. The main processes of an insurance company (product development, underwriting, claims settlement, investments) are presented. Marketing and distribution are also described. Part IV (chapters 26 to 35) defines the financial statement and introduces IFRS principles. Solvency II calculation, ALM model, and Embedded Value are explained in detail. This part also describes management accounting, performance indicators, and the Business Plan in the insurance industry. The book offers a valuable resource for lower and upper undergraduate students, graduate students, professionals/practitioners working at insurance companies, insurance agents, brokers, bankers, and consultants.
Fundamentals of the Theory of Mechanical Vibrations
by Rubens Gonçalves Salsa JuniorThis book presents the fundamental concepts of modeling and analysis of vibrations in mechanical systems with one or more degrees of freedom. The presentation of classic topics is enriched by discussions on equilibrium, stability, and the linearization of the equations of motion. Practical examples throughout the text illustrate the applicability of the theory and explore the physics behind the equations. This book includes various Matlab codes, which allow readers to modify parameters and investigate the behavior of a wide range of mechanical systems. Furthermore, it is demonstrated how some of the mechanical systems studied can be constructed using ordinary materials, enabling readers to compare the theoretical results predicted by the mathematical models with the actual observed behavior.
Fundamentals of van der Waals and Casimir Interactions (Springer Series on Atomic, Optical, and Plasma Physics #102)
by Bo E. SerneliusThis book presents a self-contained derivation of van der Waals and Casimir type dispersion forces, covering the interactions between two atoms but also between microscopic, mesoscopic, and macroscopic objects of various shapes and materials. It also presents detailed and general prescriptions for finding the normal modes and the interactions in layered systems of planar, spherical and cylindrical types, with two-dimensional sheets, such as graphene incorporated in the formalism. A detailed derivation of the van der Waals force and Casimir-Polder force between two polarizable atoms serves as the starting point for the discussion of forces: Dispersion forces, of van der Waals and Casimir type, act on bodies of all size, from atoms up to macroscopic objects. The smaller the object the more these forces dominate and as a result they play a key role in modern nanotechnology through effects such as stiction. They show up in almost all fields of science, including physics, chemistry, biology, medicine, and even cosmology. Written by a condensed matter physicist in the language of condensed matter physics, the book shows readers how to obtain the electromagnetic normal modes, which for metallic systems, is especially useful in the field of plasmonics.
Funktionalanalysis: Topologische Raume, Funktionentheorie, Gewohnliche Differentialgleichungen, Maß- Und Integrationstheorie, Funktionalanalysis ... Literaturverzeichnis. (Springer-lehrbuch)
by Dirk WernerIn dieser leicht lesbaren und gründlichen Einführung in die Funktionalanalysis behandelt der Autor neben dem Standardlehrstoff auch Themen wie Interpolation linearer Operatoren, die Schwartzsche Distributionentheorie oder die GNS-Darstellung von C*-Algebren. Im Anhang ist das notwendige Wissen zu Lebesgue-Integralen sowie metrischen und topologischen Räumen zusammengefasst. Die korrigierte Neuauflage bietet über 200, zum Teil neue Aufgaben mit Anleitungen und Lösungen. Ideal als Vorlesungsgrundlage im Mathematik- und Physikstudium.
Funktionen für Höhlenmenschen und andere Anfänger: Koordinatensysteme zur Darstellung von Abhängigkeiten in der Mathematik (essentials)
by Jürgen BeetzFunktionen und Koordinatensysteme spielen in der Mathematik eine wichtige Rolle - und im täglichen Leben auch. Meist merken wir es gar nicht oder sind uns über die mathematischen Hintergründe von Grafiken gar nicht klar, die wir in den Medien sehen. Deswegen werden in diesem Essential die Grundlagen dieser bedeutenden Werkzeuge des Denkens dargestellt und ihre Verwendung illustriert. Da dazu auch ihr Missbrauch gehört, wird auch das Thema ,,Lügen mit Grafiken" behandelt: falsche Maßstäbe, Unterdrückung des Nullpunkts, unsinnige Extrapolationen und schließlich Fehler in den Zahlen selbst.