Linear Algebra
Linear Algebra

Author: Fernando Barrera-Mora

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-05-08

Total Pages: 342

ISBN-13: 3111136140

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There are numerous linear algebra textbooks available on the market. Yet, there are few that approach the notion of eigenvectors and eigenvalues across an operator's minimum polynomial. In this book, we take that approach. This book provides a thorough introduction to the fundamental concepts of linear algebra. The material is divided into two sections: Part I covers fundamental concepts in linear algebra, whereas Part II covers the theory of determinants, the theory of eigenvalues and eigenvectors, and fundamental results on Euclidean vector spaces. We highlight that: Consider hypothetical manufacturing models as a starting point for studying linear equations. There are two novel ideas in the book: the use of a production model to motivate the concept of matrix product and the use of an operator's minimal polynomial to describe the theory of eigenvalues and eigenvectors. Several examples incorporate the use of SageMath., allowing the reader to focus on conceptual comprehension rather than formulas.

Differential Equations and Boundary Value Problems
Differential Equations and Boundary Value Problems

Author: Charles Henry Edwards

Publisher: Pearson Educación

Published: 2000

Total Pages: 816

ISBN-13: 9789684444386

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For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course while maintaining the solid foundation of algebraic techniques that are still essential to science and engineering students. It reflects the new excitement in differential equations as the availability of technical computing environments likeMaple, Mathematica, and MATLAB reshape the role and applications of the discipline. New technology has motivated a shift in emphasis from traditional, manual methods to both qualitative and computer-based methods that render accessible a wider range of realistic applications. With this in mind, the text augments core skills with conceptual perspectives that students will need for the effective use of differential equations in their subsequent work and study.

Berkeley Problems in Mathematics
Berkeley Problems in Mathematics

Author: Paulo Ney de Souza

Publisher: Springer Science & Business Media

Published: 2004-01-08

Total Pages: 614

ISBN-13: 9780387204291

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This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.

Probability Theory and Mathematical Statistics for Engineers
Probability Theory and Mathematical Statistics for Engineers

Author: V. S. Pugachev

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 469

ISBN-13: 1483190501

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Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables. The book underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vectors and their distributions, including conditional distributions of projections of a random vector, conditional numerical characteristics, and information contained in random variables. The book elaborates on the functions of random variables and estimation of parameters of distributions. Topics include frequency as a probability estimate, estimation of statistical characteristics, estimation of the expectation and covariance matrix of a random vector, and testing the hypotheses on the parameters of distributions. The text then takes a look at estimator theory and estimation of distributions. The book is a vital source of data for students, engineers, postgraduates of applied mathematics, and other institutes of higher technical education.