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Author: Alvan R. Feinstein
Publisher:
ISBN: 9780300241792
Category : Electronic books
Languages : en
Pages :
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Book Description
Author: Alvan R. Feinstein
Publisher:
ISBN: 9780300241792
Category : Electronic books
Languages : en
Pages :
Get Book Here
Book Description
Author: Leon Simon
Publisher: Morgan & Claypool Publishers
ISBN: 159829802X
Category : Technology & Engineering
Languages : en
Pages : 142
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Book Description
The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in the first ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds. The book then concludes with further essential linear algebra, including the theory of determinants, eigenvalues, and the spectral theorem for real symmetric matrices, and further multivariable analysis, including the contraction mapping principle and the inverse and implicit function theorems. There is also an appendix which provides a nine-lecture introduction to real analysis. There are various ways in which the additional material in the appendix could be integrated into a course--for example in the Stanford Mathematics honors program, run as a four-lecture per week program in the Autumn Quarter each year, the first six lectures of the nine-lecture appendix are presented at the rate of one lecture per week in weeks two through seven of the quarter, with the remaining three lectures per week during those weeks being devoted to the main chapters of the text. It is hoped that the text would be suitable for a quarter or semester course for students who have scored well in the BC Calculus advanced placement examination (or equivalent), particularly those who are considering a possible major in mathematics. The author has attempted to make the presentation rigorous and complete, with the clarity and simplicity needed to make it accessible to an appropriately large group of students. Table of Contents: Linear Algebra / Analysis in R / More Linear Algebra / More Analysis in R / Appendix: Introductory Lectures on Real Analysis
Author: Sadanori Konishi
Publisher: CRC Press
ISBN: 1466567287
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Select the Optimal Model for Interpreting Multivariate Data Introduction to Multivariate Analysis: Linear and Nonlinear Modeling shows how multivariate analysis is widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Along with the basic concepts of various procedures in traditional multivariate analysis, the book covers nonlinear techniques for clarifying phenomena behind observed multivariate data. It primarily focuses on regression modeling, classification and discrimination, dimension reduction, and clustering. The text thoroughly explains the concepts and derivations of the AIC, BIC, and related criteria and includes a wide range of practical examples of model selection and evaluation criteria. To estimate and evaluate models with a large number of predictor variables, the author presents regularization methods, including the L1 norm regularization that gives simultaneous model estimation and variable selection. For advanced undergraduate and graduate students in statistical science, this text provides a systematic description of both traditional and newer techniques in multivariate analysis and machine learning. It also introduces linear and nonlinear statistical modeling for researchers and practitioners in industrial and systems engineering, information science, life science, and other areas.
Author: Mitchell H. Katz
Publisher: Cambridge University Press
ISBN: 9780521549851
Category : Medical
Languages : en
Pages : 228
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Book Description
How to perform and interpret multivariable analysis, using plain language rather than complex derivations.
Author: Griffith B. Price
Publisher: Springer Science & Business Media
ISBN: 1461252288
Category : Mathematics
Languages : en
Pages : 668
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Book Description
This book contains an introduction to the theory of functions, with emphasis on functions of several variables. The central topics are the differentiation and integration of such functions. Although many of the topics are familiar, the treatment is new; the book developed from a new approach to the theory of differentiation. Iff is a function of two real variables x and y, its deriva tives at a point Po can be approximated and found as follows. Let PI' P2 be two points near Po such that Po, PI, P2 are not on a straight line. The linear function of x and y whose values at Po, PI' P2 are equal to those off at these points approximates f near Po; determinants can be used to find an explicit representation of this linear function (think of the equation of the plane through three points in three-dimensional space). The (partial) derivatives of this linear function are approximations to the derivatives of f at Po ; each of these (partial) derivatives of the linear function is the ratio of two determinants. The derivatives off at Po are defined to be the limits of these ratios as PI and P2 approach Po (subject to an important regularity condition). This simple example is only the beginning, but it hints at a m theory of differentiation for functions which map sets in IRn into IR which is both general and powerful, and which reduces to the standard theory of differentiation in the one-dimensional case.
Author: Brian Everitt
Publisher: Springer Science & Business Media
ISBN: 1441996508
Category : Mathematics
Languages : en
Pages : 284
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Book Description
The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.
Author: Satish Shirali
Publisher: Springer Science & Business Media
ISBN: 0857291920
Category : Mathematics
Languages : en
Pages : 399
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Book Description
This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are expounded in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz' Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selection of problems, ranging from simple to more challenging, are included with carefully formed solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.
Author: Piotr Mikusinski
Publisher: Springer Science & Business Media
ISBN: 1461200733
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This book takes the student and researcher on a journey through the core topics of the subject. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible. Good bibliography and index.
Author: T. W. Anderson
Publisher: Wiley-Interscience
ISBN: 9780471360919
Category : Business & Economics
Languages : en
Pages : 721
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Book Description
Perfected over three editions and more than forty years, this field- and classroom-tested reference: * Uses the method of maximum likelihood to a large extent to ensure reasonable, and in some cases optimal procedures. * Treats all the basic and important topics in multivariate statistics. * Adds two new chapters, along with a number of new sections. * Provides the most methodical, up-to-date information on MV statistics available.
Author: Kurt Varmuza
Publisher: CRC Press
ISBN: 1420059491
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Using formal descriptions, graphical illustrations, practical examples, and R software tools, Introduction to Multivariate Statistical Analysis in Chemometrics presents simple yet thorough explanations of the most important multivariate statistical methods for analyzing chemical data. It includes discussions of various statistical methods, such as
