Kirjahaku

This book offers an intuitive approach to random processes and educates the reader on how to interpret and predict their behavior. Premised on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is easier to comprehend and more enjoyable, and it motivates the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data--e.g., a time series about which nothing is known a priori--and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the Wiener-Khintchine theory), and the latter applies and interprets them in specific physical contexts. The formidable Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent, and gradually extended to the full-blown iterative matrix form.

This book offers an intuitive approach to random processes and educates the reader on how to interpret and predict their behavior. Premised on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is easier to comprehend and more enjoyable, and it motivates the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data--e.g., a time series about which nothing is known a priori--and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the Wiener-Khintchine theory), and the latter applies and interprets them in specific physical contexts. The formidable Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent, and gradually extended to the full-blown iterative matrix form.

This book presents a short introduction to the main tools of optimization methodology including linear programming, steepest descent, conjugate gradients, and the Karush-Kuhn-Tucker-John conditions. Each topic is developed in terms of a specific physical model, so that the strategy behind every step is motivated by a logical, concrete, easily visualized objective. A quick perusal of the Fibonacci search algorithm provides a simple and tantalizing first encounter with optimization theory, and a review of the max-min exposition of one-dimensional calculus prepares readers for the more sophisticated topics found later in the book. Notable features are the innovative perspectives on the simplex algorithm and Karush-Kuhn-Tucker-John conditions as well as a wealth of helpful diagrams. The author provides pointers to references for readers who would like to learn more about rigorous definitions, proofs, elegant reformulations and extensions, and case studies. However, the book is sufficiently self-contained to serve as a reliable resource for readers who wish to exploit commercially available optimization software without investing the time to develop expertise in its aspects.This book also:Features innovative perspectives on the simplex algorithm and Krushal-Kuhn-Tucker-John conditionsServes as a resource for readers to use the tools of optimization without needing to acquire expertise in the theoryFeatures plentiful resources that focus on rigorous definitions, proofs, and case studies

This book provides readers with an introductory overview of art from the perspective of science, technology, engineering, and mathematics. The author utilizes well-known and important works of art to demonstrate how STEM concepts apply to them. The book’s examples include a structural analysis of Michelangelo’s David. The author covers major breakthroughs in art history, such as the discovery of perspective. The book also discusses other important elements of art, such as color, from a scientific point of view. The author ensures that readers will understand the art terms used by comparing them with terms used in STEM fields of study.

This book presents a short introduction to the main tools of optimization methodology including linear programming, steepest descent, conjugate gradients, and the Karush-Kuhn-Tucker-John conditions. Each topic is developed in terms of a specific physical model, so that the strategy behind every step is motivated by a logical, concrete, easily visualized objective. A quick perusal of the Fibonacci search algorithm provides a simple and tantalizing first encounter with optimization theory, and a review of the max-min exposition of one-dimensional calculus prepares readers for the more sophisticated topics found later in the book. Notable features are the innovative perspectives on the simplex algorithm and Karush-Kuhn-Tucker-John conditions as well as a wealth of helpful diagrams. The author provides pointers to references for readers who would like to learn more about rigorous definitions, proofs, elegant reformulations and extensions, and case studies. However, the book is sufficiently self-contained to serve as a reliable resource for readers who wish to exploit commercially available optimization software without investing the time to develop expertise in its aspects. This book also: Features innovative perspectives on the simplex algorithm and Krushal-Kuhn-Tucker-John conditions Serves as a resource for readers to use the tools of optimization without needing to acquire expertise in the theory Features plentiful resources that focus on rigorous definitions, proofs, and case studies

This set includes Fundamentals of Matrix Analysis with Applications & Solutions Manual to Accompany Fundamentals of Matrix Analysis with Applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applicationsCoverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficientsChapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts

Solutions Manual to accompany Fundamentals of Matrix Analysis with Applications—an accessible and clear introduction to linear algebra with a focus on matrices and engineering applications.

Matrix Fundamentals introduces tools for working with matrices, their applications, and their significance in the broader context of linear algebra. Assuming no previous exposure to matrices, the first four chapters provide a foundation accessible to students with a basic knowledge of calculus, covering essential matrix methods used in various quantitative fields. The book formulates algorithms and discusses their practical implementation. Later chapters introduce more advanced topics, such as singular value decomposition, along with some modern applications. Emphasizing visualization and experimentation, this text is designed for undergraduate courses for students in STEM, as well as business, economics and social sciences.