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Praktische Mathematik für Ingenieure und Physiker

Praktische Mathematik für Ingenieure und Physiker

Praktische Mathematik für Ingenieure und Physiker

426 man fordert also Anfangs- und Endordinate der Lösung y (x) im Inter­ vall (a, b), Abb. 112. An Stelle der Randordinaten (sogenannte erste Randwertaufgabe) lassen sich auch die Randsteigungen y' (a), y' (b) . Y fordern (zweite Randwertaufgabe) oder schließ­ lich eine Linearkombination zwischen Ordinaten und Steigungen (dritte Randwertaufgabe). Alle jl diese Aufgaben oder auch ihre Kombinationen treten in den Anwendungen auf. . :c Ähnlich wie bei der Anfangswertaufgabe wird Abb. 112 Zur Randwertaufgabe man bei formelmäßiger Lösung versuchen, die in der allgemeinen Lösung enthaltenen freien Integratlonskonstanten aus den beiden Randbedingungen zu bestimmen und so die fragliche Sonderlösung y(x) festzulegen. Prinzipiell scheint sich gegenüber der Anfangswertaufgabe damit kaum etwas geändert zu haben. Bei der Durchführung derartiger Aufgaben aber zeigt sich sehr bald, daß sie im Gegensatz zur Anfangswertaufgabe nicht mehr in jedem Falle lösbar sind. Es treten hier also neue charakteristische Schwierigkeiten auf, zu deren Überwindung besondere Überlegungen notwendig werden. Aber auch die Behandlungsmethoden, insbesondere die uns vornehmlich interessierenden Näherungsverfahren, sind von denen der Anfangswertaufgaben grundverschieden, so daß wir es hier in der Tat mit einem neuen und im übrigen höchst reizvollen Gebiet der praktischen Mathematik zu tun haben, bei dem auch theoretische Fragen mehr als bisher in den Vordergrund treten werden. Die charakteristische Schwierigkeit des Randwertproblems sei an folgendem einfachen Beispiel erläutert. 1. Beispiel: Gegeben sei die - lineare - Differentialgleichung y" + y = 0 mit den Randbedingungen y(O) = 1, y(2) = O.

Praktische Mathematik für Ingenieure und Physiker

Traffic and Granular Flow 2019 (Springer Proceedings in Physics #252)

This book gathers contributions on a variety of flowing collective systems. While primarily focusing on pedestrian dynamics, they also reflect the latest developments in areas such as vehicular traffic and granular flows and address related emerging topics such as self-propelled particles, data transport, swarm behavior, intercellular transport, and collective dynamics of biological systems. Combining fundamental research and practical applications in the various fields discussed, the book offers a valuable asset for researchers and practitioners alike.

Representations of Fundamental Groups of Algebraic Varieties (Lecture Notes in Mathematics #1708)

Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.

Pseudodifferential Equations Over Non-Archimedean Spaces (Lecture Notes in Mathematics #2174)

Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applications of p-adic wavelets.

Applications of Graph Transformations with Industrial Relevance: Third International Symposium, AGTIVE 2007, Kassel, Germany, October 10-12, 2007, Revised Selected and Invited Papers (Lecture Notes in Computer Science #5088)

This book constitutes the thoroughly refereed post-conference proceedings of the Third International Symposium on Applications of Graph Transformations, AGTIVE 2007, held in Kassel, Germany, in October 2007. The 30 revised full papers presented together with 2 invited papers were carefully selected from numerous submissions during two rounds of reviewing and improvement. The papers are organized in topical sections on graph transformation applications, meta-modeling and domain-specific language, new graph transformation approaches, program transformation applications, dynamic system modeling, model driven software development applications, queries, views, and model transformations, as well as new pattern matching and rewriting concepts. The volume moreover contains 4 papers resulting from the adjacent graph transformation tool contest and concludes with 9 papers summarizing the state of the art of today's available graph transformation environments.

Zur Theorie der Funktionen mehrerer komplexer Veränderlichen: Die Automorphismen der unbeschränkten eigentlichen Kreiskörper

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Parallel Multilevel Methods: Adaptive Mesh Refinement and Loadbalancing (Advances in Numerical Mathematics)

Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are covered from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.

Understanding and Investigating Response Processes in Validation Research (Social Indicators Research Series #69)

This volume addresses an urgent need across multiple disciplines to broaden our understanding and use of response processes evidence of test validity. It builds on the themes and findings of the volume Validity and Validation in Social, Behavioral, and Health Sciences (Zumbo & Chan, 2014), with a focus on measurement validity evidence based on response processes. Approximately 1000 studies are published each year examining the validity of inferences made from tests and measures in the social, behavioural, and health sciences. The widely accepted Standards for Educational and Psychological Testing (1999, 2014) present five sources of evidence for validity: content-related, response processes, internal structure, relationships with other variables, and consequences of testing. Many studies focus on internal structure and relationships with other variables sources of evidence, which have a long history in validation research, known methodologies, and numerous exemplars in the literature. Far less is understood by test users and researchers conducting validation work about how to think about and apply new and emerging sources of validity evidence. This groundbreaking volume is the first to present conceptual models of response processes, methodological issues that arise in gathering response processes evidence, as well as applications and exemplars for providing response processes evidence in validation work.

Discrete Time Series, Processes, and Applications in Finance (Springer Finance)

Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts. This book presents a survey of the empirical properties of financial time series, their descriptions by means of mathematical processes, and some implications for important financial applications used in many areas like risk evaluation, option pricing or portfolio construction. The statistical tools used to extract information from raw data are introduced. Extensive multiscale empirical statistics provide a solid benchmark of stylized facts (heteroskedasticity, long memory, fat-tails, leverage…), in order to assess various mathematical structures that can capture the observed regularities. The author introduces a broad range of processes and evaluates them systematically against the benchmark, summarizing the successes and limitations of these models from an empirical point of view. The outcome is that only multiscale ARCH processes with long memory, discrete multiplicative structures and non-normal innovations are able to capture correctly the empirical properties. In particular, only a discrete time series framework allows to capture all the stylized facts in a process, whereas the stochastic calculus used in the continuum limit is too constraining. The present volume offers various applications and extensions for this class of processes including high-frequency volatility estimators, market risk evaluation, covariance estimation and multivariate extensions of the processes. The book discusses many practical implications and is addressed to practitioners and quants in the financial industry, as well as to academics, including graduate (Master or PhD level) students. The prerequisites are basic statistics and some elementary financial mathematics.

Numerische Mathematik: Eine Einführung anhand von Differentialgleichungsproblemen Band 2: Instationäre Probleme (Mathematik Kompakt)

"Numerische Mathematik", in zwei Bänden, ist eine Einführung in die Numerische Mathematik anhand von Differenzialgleichungsproblemen. Gegliedert nach elliptischen, parabolischen und hyperbolischen Differenzialgleichungen, erläutert sie zunächst jeweils die Diskretisierung solcher Probleme. Als Diskretisierungstechniken stehen Finite-Elemente-Methoden im Raum und (partitionierte) Runge-Kutta-Methoden in der Zeit im Vordergrund. Die diskretisierten Gleichungen motivieren die Diskussion von Methoden für endlichdimensionale (nicht)lineare Gleichungen, die anschließend als eigenständige Themen behandelt werden. Ein in sich geschlossenes Bild.

Numerische Mathematik: Eine Einführung anhand von Differentialgleichungsproblemen; Band 1: Stationäre Probleme (Mathematik Kompakt)

"Numerik", in zwei Bänden, ist eine Einführung in die Numerische Mathematik anhand von Differenzialgleichungsproblemen. Gegliedert nach elliptischen, parabolischen und hyperbolischen Differenzialgleichungen, erläutert sie zunächst jeweils die Diskretisierung solcher Probleme. Als Diskretisierungstechniken stehen Finite-Elemente-Methoden im Raum und (partitionierte) Runge-Kutta-Methoden in der Zeit im Vordergrund. Die diskretisierten Gleichungen motivieren die Diskussion von Methoden für endlichdimensionale (nicht)lineare Gleichungen, die anschließend als eigenständige Themen behandelt werden. Ein in sich geschlossenes Bild.

Theorie der Eröffnungen der 807 Partieen der ersten sechs Jahrgänge der Neuen Berliner Schachzeitung: Kürzester Leitfaden des Schachspiels

Reference Frames for Applications in Geosciences (International Association of Geodesy Symposia #138)

Reference systems and frames are of primary importance for many Earth science applications, satellite navigation as well as for practical applications in geo-information. A precisely defined reference frame is needed for the quantification of, e.g. Earth rotation and its gravity field, global and regional sea level variation, tectonic motion and deformation, post-glacial rebound, geocenter motion, large scale deformation due to Earthquakes, local subsidence and other ruptures and crustal dislocations. All of these important scientific applications fundamentally depend on a truly global reference system that only space geodesy can realize. This volume details the proceedigns of the IAG Symposium REFAG2010 (Marne la Vallée, France, October 4-8, 2010) The primary scope of REFAG2010 was to address today’s achievements on theoretical concepts of reference systems and their practical implementations by individual space geodetic techniques and their combinations, underlying limiting factors, systematic errors and novel approaches for future improvements.

Computing the Optical Properties of Large Systems (Springer Theses)

This work addresses the computation of excited-state properties of systems containing thousands of atoms. To achieve this, the author combines the linear response formulation of time-dependent density functional theory (TDDFT) with linear-scaling techniques known from ground-state density-functional theory. This extends the range of TDDFT, which on its own cannot tackle many of the large and interesting systems in materials science and computational biology. The strengths of the approach developed in this work are demonstrated on a number of problems involving large-scale systems, including exciton coupling in the Fenna-Matthews-Olson complex and the investigation of low-lying excitations in doped p-terphenyl organic crystals.

Non-equilibrium Evaporation and Condensation Processes: Analytical Solutions (Mathematical Engineering)

This monograph presents a comprehensive treatment of analytical solutions to problems in the area of non-equilibrium evaporation and condensation processes. The book covers, among others, topics such as systems of conversation equations for molecular fluxes of mass, momentum and energy within the Knudsen layer, spherical growth of vapor bubbles in volumes of highly superheated liquid. The target audience primarily comprises research experts in the field of thermodynamics and fluid dynamics, but the book may also be beneficial for graduate students alike.

Non-equilibrium Evaporation and Condensation Processes: Analytical Solutions (Mathematical Engineering)

This monograph is focused mostly on the exposition of analytical methods for the solution of problems of strong phase change. A new theoretical model is proved useful in describing, with acceptable accuracy, problems of strong evaporation and condensation. The book is the first to treat the problem of asymmetry for evaporation/condensation. A semi-empirical model for the process is proposed for purposes of practical calculation of the process of strong evaporation. The “limiting schemes” of the vapor bubble growth are analyzed. The thermo-hydrodynamic problem of evaporating meniscus of a thin liquid film on a heated surface is considered. A theoretical analysis of the problem of evaporation of a drop levitating over a vapor cushion is performed. The problem of vapor condensation upon a transversal flow around a horizontal cylinder is considered. The second edition is extended by (i) the conjugate “strong evaporation - heat conduction” problem, (ii) the influence of accommodation coefficients on intensive processes of evaporation and condensation, (iii) the problem of supersonic condensation. This book is the first to present a comprehensive theoretical approach of boiling problems: nucleate boiling, superfluid helium phase transition, similarity between pseudo-boiling and subcritical pressure nucleate boiling. The target audience primarily comprises research experts in the field of thermodynamics and fluid dynamics, but the book may also be beneficial for graduate students.

Theory of Periodic Conjugate Heat Transfer (Mathematical Engineering #5)

This book provides a detailed yet comprehensive presentation of the theory of periodic conjugate heat transfer. It contains an analytical approach to the effects of thermophysical and geometrical properties of a solid body on the experimentally determined heat transfer coefficient. The main objective of the book is a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation.This third and extended edition covers Wall's thermal effect on Landau stability, gas bubbles pulsations in fluids, and also the interplay between periodic conjugate heat transfer and non-Fourier heat conduction. The target audience primarily comprises research experts in the field of thermodynamics and fluid dynamics, but the book may also be beneficial for graduate students in engineering.

Statistical Physics of Biomolecules: An Introduction

From the hydrophobic effect to protein-ligand binding, statistical physics is relevant in almost all areas of molecular biophysics and biochemistry, making it essential for modern students of molecular behavior. But traditional presentations of this material are often difficult to penetrate. Statistical Physics of Biomolecules: An Introduction brin

Abstraction, Reformulation and Approximation: 6th International Symposium, SARA 2005, Airth Castle, Scotland, UK, July 26-29, 2005, Proceedings (Lecture Notes in Computer Science #3607)

Basketball Data Science: With Applications in R (Chapman & Hall/CRC Data Science Series)

Using data from one season of NBA games, Basketball Data Science: With Applications in R is the perfect book for anyone interested in learning and applying data analytics in basketball. Whether assessing the spatial performance of an MBA player&’s shots or doing an analysis of the impact of high pressure game situations on the probability of scoring, this book discusses a variety of case studies and hands-on examples using a custom R package. The codes are supplied so readers can reproduce the analyses themselves or create their own. Assuming a basic statistical knowledge, Basketball Data Science with R is suitable for students, technicians, coaches, data analysts and applied researchers. Features: · One of the first books to provide statistical and data mining methods for the growing field of analytics in basketball. · Presents tools for modelling graphs and figures to visualize the data. · Includes real world case studies and examples, such as estimations of scoring probability using the Golden State Warriors as a test case. · Provides the source code and data so readers can do their own analyses on NBA teams and players.

Basketball Data Science: With Applications in R (Chapman & Hall/CRC Data Science Series)

Using data from one season of NBA games, Basketball Data Science: With Applications in R is the perfect book for anyone interested in learning and applying data analytics in basketball. Whether assessing the spatial performance of an MBA player&’s shots or doing an analysis of the impact of high pressure game situations on the probability of scoring, this book discusses a variety of case studies and hands-on examples using a custom R package. The codes are supplied so readers can reproduce the analyses themselves or create their own. Assuming a basic statistical knowledge, Basketball Data Science with R is suitable for students, technicians, coaches, data analysts and applied researchers. Features: · One of the first books to provide statistical and data mining methods for the growing field of analytics in basketball. · Presents tools for modelling graphs and figures to visualize the data. · Includes real world case studies and examples, such as estimations of scoring probability using the Golden State Warriors as a test case. · Provides the source code and data so readers can do their own analyses on NBA teams and players.

Statistik für Bachelor- und Masterstudenten: Eine Einführung für Wirtschafts- und Sozialwissenschaftler (Statistik und ihre Anwendungen)

Das Buch führt in die wesentlichen statistischen Konzepte und Ideen ein und erläutert anhand von Beispielen detailliert deren Umsetzung. Der Stil ist, anders als bei den meisten Konkurrenzwerken, betont locker gehalten - ohne dabei auf eine exakte Darstellung zu verzichten. Das Buch ist speziell auf die Bedürfnisse von Anfängern im Fach Statistik zugeschnitten und für Bachelor- und Masterstudenten aller Disziplinen geeignet – auch zum Selbststudium.