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The Linear Algebra a Beginning Graduate Student Ought to Know - Jonathan S. Golan - Bog - Springer - Plusbog.dk

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.

DKK 646.00

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Magnetic Components - Peter Zacharias - Bog - Springer - Plusbog.dk

The book deals with methods for the description and design of electromagnetic components. Both linear and nonlinear components are covered. For electrical simulations the necessary equivalent circuit diagrams are derived and a general methodology is developed. Possible influences on properties via material selection, winding design and premagnetisation of sections are treated. Measurement characterization, modeling, possible errors and model limits are dealt with extensively. In the last chapter examples are discussed.

DKK 519.00

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Stochastic Modelling and Control - Mark Davis - Bog - Springer - Plusbog.dk

This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a ''black box'' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.

DKK 731.00

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Random Fields for Spatial Data Modeling - Dionissios T. Hristopulos - Bog - Springer - Plusbog.dk

This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means ofmodels based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatialdata analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

DKK 1089.00

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Geometry - Intuition and Concepts - Jost Hinrich Eschenburg - Bog - Springer - Plusbog.dk

This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one''s eyes. Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1 st edition Geometrie - Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

DKK 689.00

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Functional Analysis - Leonid P. Lebedev - Bog - Springer - Plusbog.dk

This book started its life as a series of lectures given by the second author from the 1970''s onwards to students in their third and fourth years in the Department of Mathematics at the Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that stage the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them.

DKK 663.00

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Octave and MATLAB for Engineering Applications - Andreas Stahel - Bog - Springer - Plusbog.dk

For many engineering tasks extensive computations or visualizations are required. The well established Matlab and Octave (a very similar open source software) are excellent tools for modeling, computing and visualization. This book will help the reader to acquire basic knowledge and elementary programming skills with Octave/Matlab. Basic data and programming structures are presented and for the most often used commands illustrative code samples are provided. The selection of the presented commands is guided by the typical needs of engineers. With these skills many and more difficult problems can be solved successfully. It is shown how basic statistical questions can be answered and how results are visualized using appropriate types of graphical representation. A selection of typical, independent engineering problems is presented, together with algorithms to solve these problems. Special attention is given to the methods of linear and nonlinear regression. The high level tool Matlab/Octave is used to develop computational code for micro controllers. The codes and data files for the book are available on Github and on Springer Link. The Target Groups - Students in electrical and mechanical engineering and engineering fields in general - Working engineers

DKK 604.00

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Mathematics for Computer Scientists - Peter Hartmann - Bog - Springer - Plusbog.dk

This textbook contains the mathematics needed to study computer science in application-oriented computer science courses. The content is based on the author''s many years of teaching experience. The translation of the original German 7 th edition Mathematik für Informatiker by Peter Hartmann was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content. Textbook Features - You will always find applications to computer science in this book. - Not only will you learn mathematical methods, you will gain insights into the ways of mathematical thinking to form a foundation for understanding computer science. - Proofs are given when they help you learn something, not for the sake of proving. Mathematics is initially a necessary evil for many students. The author explains in each lesson how students can apply what they have learned by giving many real world examples, and by constantly cross-referencing math and computer science. Students will see how math is not only useful, but can be interesting and sometimes fun. The Content - Sets, logic, number theory, algebraic structures, cryptography, vector spaces, matrices, linear equations and mappings, eigenvalues, graph theory. - Sequences and series, continuous functions, differential and integral calculus, differential equations, numerics. - Probability theory and statistics. The Target Audiences Students in all computer science-related coursework, and independent learners.

DKK 526.00

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SPSS for Starters, Part 2 - Ton J. Cleophas - Bog - Springer - Plusbog.dk

The first part of this title contained all statistical tests that are relevant for starters on SPSS, and included standard parametric and non-parametric tests for continuous and binary variables, regression methods, trend tests, and reliability and validity assessments of diagnostic tests. The current part 2 of this title reviews multistep methods, multivariate models, assessments of missing data, performance of diagnostic tests, meta-regression, Poisson regression, confounding and interaction, and survival analyses using log tests and segmented time-dependent Cox regression. Methods for assessing non linear models, data seasonality, distribution free methods, including Monte Carlo methods and artificial intelligence, and robust tests are also covered. Each method of testing is explained using a data example from clinical practice,including every step in SPSS, and a text with interpretations of the results and hints convenient for data reporting. In order to facilitate the use of this cookbook the data files of the examples is made available by the editor through extras.springer.com. Both part 1 and 2 of this title contain a minima amount of text and maximal technical details, but we believe that this property will not refrain students from mastering the SPSS software systematics, and that, instead, it will be a help to that aim. Yet, we recommend that it will used together with the textbook "Statistics Applied to Clinical Trials" (5th edition, Springer, Dordrecht 2012) and the e-books "Statistics on a Pocket Calculator Part 1 and 2 (Springer, Dordrecht, 2011 and 2012) from the same authors.

DKK 434.00

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Statistical Analysis of Clinical Data on a Pocket Calculator, Part 2 - Ton J. Cleophas - Bog - Springer - Plusbog.dk

The first part of this title contained all statistical tests relevant to starting clinical investigations, and included tests for continuous and binary data, power, sample size, multiple testing, variability, confounding, interaction, and reliability. The current part 2 of this title reviews methods for handling missing data, manipulated data, multiple confounders, predictions beyond observation, uncertainty of diagnostic tests, and the problems of outliers. Also robust tests, non-linear modeling , goodness of fit testing, Bhatacharya models, item response modeling, superiority testing, variability testing, binary partitioning for CART (classification and regression tree) methods, meta-analysis, and simple tests for incident analysis and unexpected observations at the workplace and reviewed. Each test method is reported together with (1) a data example from practice, (2) all steps to be taken using a scientific pocket calculator, and (3) the main results and their interpretation. Although several of the described methods can also be carried out with the help of statistical software, the latter procedure will be considerably slower. Both part 1 and 2 of this title consist of a minimum of text and this will enhance the process of mastering the methods. Yet the authors recommend that for a better understanding of the test procedures the books be used together with the same authors'' textbook "Statistics Applied to Clinical Studies" 5th edition edited 2012, by Springer Dordrecht Netherlands. More complex data files like data files with multiple treatment modalities or multiple predictor variables can not be analyzed with a pocket calculator. We recommend that the small books "SPSS for starters", Part 1 and 2 (Springer, Dordrecht, 2010, and 2012) from the same authors be used as a complementary help for the readers'' benefit.

DKK 434.00

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