Search results for: essential-linear-algebra-with-applications

Essential Linear Algebra with Applications

Author : Titu Andreescu
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Rooted in a pedagogically successful problem-solving approach to linear algebra, the present work fills a gap in the literature that is sharply divided between elementary texts and books that are too advanced to appeal to a wide audience. It clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. Ideal as an introduction to linear algebra, the extensive exercises and well-chosen applications also make this text suitable for advanced courses at the junior or senior undergraduate level. Furthermore, it can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, "Essential Linear Algebra with Applications" is a natural bridge between pure and applied mathematics and the natural and social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject’s hallmark.

Essential Linear Algebra

Author : Jared M. Maruskin
File Size : 26.85 MB
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This text introduces linear algebra-boiled to its essence-presented in a clear and concise fashion. Designed around a single-semester undergraduate course, Essential Linear Algebra introduces key concepts, various real-world applications, and provides detailed yet understandable proofs of key results that are aimed towards students with no advanced preparation in proof writing. The level of sophistication gradually increases from beginning to end in order to prepare students for subsequent studies.

Introductory Linear Algebra with Applications

Author : Bernard Kolman
File Size : 32.13 MB
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Matrix Algebra

Author : James E. Gentle
File Size : 39.7 MB
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Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Basic Linear Algebra with Applications

Author : Garfield C. Schmidt
File Size : 45.62 MB
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Linear Algebra with Applications Alternate Edition

Author : Gareth Williams
File Size : 79.26 MB
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Part of the new Digital Filmmaker Series! Digital Filmmaking: An Introductionis the first book in the newDigital Filmmaker Series. Designed for an introductory level course in digital filmmaking, it is intended for anyone who has an interest in telling stories with pictures and sound and won't assume any familiarity with equipment or concepts on the part of the student. In addition to the basics of shooting and editing, different story forms are introduced from documentary and live events through fictional narratives. Each of the topics is covered in enough depth to allow anyone with a camera and a computer to begin creating visual projects of quality.

Numerical Linear Algebra for Applications in Statistics

Author : James E. Gentle
File Size : 27.14 MB
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Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Principles of Linear Algebra with Mathematica

Author : Kenneth M. Shiskowski
File Size : 47.52 MB
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A hands-on introduction to the theoretical and computationalaspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationallyintensive, and computer algebra systems such as Mathematica®are essential not only for learning to apply the concepts tocomputationally challenging problems, but also for visualizing manyof the geometric aspects within this field of study. Principles ofLinear Algebra with Mathematica uniquely bridges the gap betweenbeginning linear algebra and computational linear algebra that isoften encountered in applied settings, and the commands required tosolve complex and computationally challenging problems usingMathematica are provided. The book begins with an introduction to the commands andprogramming guidelines for working with Mathematica. Next, theauthors explore linear systems of equations and matrices,applications of linear systems and matrices, determinants,inverses, and Cramer's rule. Basic linear algebra topics, such asvectors, dot product, cross product, and vector projection areexplored, as well as a unique variety of more advanced topicsincluding rotations in space, 'rolling' a circle along a curve, andthe TNB Frame. Subsequent chapters feature coverage of lineartransformations from Rn to Rm, the geometry of linear and affinetransformations, with an exploration of their effect on arclength,area, and volume, least squares fits, and pseudoinverses. Mathematica is used to enhance concepts and is seamlesslyintegrated throughout the book through symbolic manipulations,numerical computations, graphics in two and three dimensions,animations, and programming. Each section concludes with standardproblems in addition to problems that were specifically designed tobe solved with Mathematica, allowing readers to test theircomprehension of the presented material. All related Mathematicacode is available on a corresponding website, along with solutionsto problems and additional topical resources. Extensively class-tested to ensure an accessible presentation,Principles of Linear Algebra with Mathematica is an excellent bookfor courses on linear algebra at the undergraduate level. The bookis also an ideal reference for students and professionals who wouldlike to gain a further understanding of the use of Mathematica tosolve linear algebra problems.

Linear Algebra with Applications

Author : John T. Scheick
File Size : 63.43 MB
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Designed for the second level course in linear algebra taken by your junior- or senior-level mathematics, engineering, or science majors, this text focuses on the fundamentals of linear algebra in a thematic framework which emphasizes concepts most important to applied mathematics, engineering, and science.

Linear Algebra Theory and Applications

Author : Kenneth Kuttler
File Size : 83.90 MB
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This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.

Solutions Manual to Accompany Linear Algebra

Author : Richard C. Penney
File Size : 61.97 MB
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This Student Solutions Manual to Accompany Linear Algebra: Ideas and Applications, Fourth Edition contains solutions to the odd numbered problems to further aid in reader comprehension, and an Instructor's Solutions Manual (inclusive of suggested syllabi) is available via written request to the Publisher. Both the Student and Instructor Manuals have been enhanced with further discussions of the applications sections, which is ideal for readers who wish to obtain a deeper knowledge than that provided by pure algorithmic approaches. Linear Algebra: Ideas and Applications, Fourth Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, this book successfully helps readers to understand not only how to implement a technique, but why its use is important.

Linear Algebra Theory and Applications

Author : Textbook Equity Edition
File Size : 39.37 MB
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This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.

Linear Algebra

Author : Jin Ho Kwak
File Size : 88.33 MB
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Linear algebra is one of the most important subjects in the study of science and engineering because of its widespread applications in social or natural science, computer science, physics, or economics. As one of the most useful courses in undergraduate mathematics, it has provided essential tools for industrial scientists. The basic concepts of linear algebra are vector spaces, linear transformations, matrices and determinants, and they serve as an abstract language for stating ideas and solving problems. This book is based on the lectures delivered several years in a sophomore level linear algebra course designed for science and engineering students. The primary purpose of this book is to give a careful presentation of the basic concepts of linear algebra as a coherent part of mathematics, and to illustrate its power and usefulness through applications to other disciplines. We have tried to emphasize the computational skills along with the mathematical abstractions, which have also an integrity and beauty of their own. The book includes a variety of interesting applications with many examples not only to help students understand new concepts but also to practice wide applications of the subject to such areas as differential equations, statistics, geometry, and physics. Some of those applications may not be central to the mathematical development and may be omitted or selected in a syllabus at the discretion of the instructor.

Elementary Linear Algebra with Applications

Author : Marc W. Konvisser
File Size : 32.86 MB
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Linear Algebra in Action

Author : Harry Dym
File Size : 86.45 MB
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Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as graduate students. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises.

Applied Linear Algebra

Author : Peter J. Olver
File Size : 20.11 MB
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This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

Linear Algebra

Author : Richard C. Penney
File Size : 52.87 MB
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This expanded new edition presents a thorough and up-to-date introduction to the study of linear algebra Linear Algebra, Third Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, the book successfully helps readers to understand not only how to implement a technique, but why its use is important. The book outlines an analytical, algebraic, and geometric discussion of the provided definitions, theorems, and proofs. For each concept, an abstract foundation is presented together with its computational output, and this parallel structure clearly and immediately illustrates the relationship between the theory and its appropriate applications. The Third Edition also features: A new chapter on generalized eigenvectors and chain bases with coverage of the Jordan form and the Cayley-Hamilton theorem A new chapter on numerical techniques, including a discussion of the condition number A new section on Hermitian symmetric and unitary matrices An exploration of computational approaches to finding eigenvalues, such as the forward iteration, reverse iteration, and the QR method Additional exercises that consist of application, numerical, and conceptual questions as well as true-false questions Illuminating applications of linear algebra are provided throughout most parts of the book along with self-study questions that allow the reader to replicate the treatments independently of the book. Each chapter concludes with a summary of key points, and most topics are accompanied by a "Computer Projects" section, which contains worked-out exercises that utilize the most up-to-date version of MATLAB(r). A related Web site features Maple translations of these exercises as well as additional supplemental material. Linear Algebra, Third Edition is an excellent undergraduate-level textbook for courses in linear algebra. It is also a valuable self-study guide for professionals and researchers who would like a basic introduction to linear algebra with applications in science, engineering, and computer science.

Solutions Manual to Accompany Linear Algebra

Author : Richard C. Penney
File Size : 84.84 MB
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This Student Solutions Manual to Accompany Linear Algebra: Ideas and Applications, Fourth Edition contains solutions to the odd numbered problems to further aid in reader comprehension, and an Instructor's Solutions Manual (inclusive of suggested syllabi) is available via written request to the Publisher. Both the Student and Instructor Manuals have been enhanced with further discussions of the applications sections, which is ideal for readers who wish to obtain a deeper knowledge than that provided by pure algorithmic approaches. Linear Algebra: Ideas and Applications, Fourth Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, this book successfully helps readers to understand not only how to implement a technique, but why its use is important.

Differential Equations with Linear Algebra

Author : Matthew R. Boelkins
File Size : 78.13 MB
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Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, the book is appropriate for courses for majors in mathematics, science, and engineering that study systems of differential equations. Because of its emphasis on linearity, the text opens with a full chapter devoted to essential ideas in linear algebra. Motivated by future problems in systems of differential equations, the chapter on linear algebra introduces such key ideas as systems of algebraic equations, linear combinations, the eigenvalue problem, and bases and dimension of vector spaces. This chapter enables students to quickly learn enough linear algebra to appreciate the structure of solutions to linear differential equations and systems thereof in subsequent study and to apply these ideas regularly. The book offers an example-driven approach, beginning each chapter with one or two motivating problems that are applied in nature. The following chapter develops the mathematics necessary to solve these problems and explores related topics further. Even in more theoretical developments, we use an example-first style to build intuition and understanding before stating or proving general results. Over 100 figures provide visual demonstration of key ideas; the use of the computer algebra system Maple and Microsoft Excel are presented in detail throughout to provide further perspective and support students' use of technology in solving problems. Each chapter closes with several substantial projects for further study, many of which are based in applications. Errata sheet available at: www.oup.com/us/companion.websites/9780195385861/pdf/errata.pdf

Computational Mathematics Numerical Analysis and Applications

Author : Mariano Mateos
File Size : 33.51 MB
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The first part of this volume gathers the lecture notes of the courses of the “XVII Escuela Hispano-Francesa”, held in Gijón, Spain, in June 2016. Each chapter is devoted to an advanced topic and presents state-of-the-art research in a didactic and self-contained way. Young researchers will find a complete guide to beginning advanced work in fields such as High Performance Computing, Numerical Linear Algebra, Optimal Control of Partial Differential Equations and Quantum Mechanics Simulation, while experts in these areas will find a comprehensive reference guide, including some previously unpublished results, and teachers may find these chapters useful as textbooks in graduate courses. The second part features the extended abstracts of selected research work presented by the students during the School. It highlights new results and applications in Computational Algebra, Fluid Mechanics, Chemical Kinetics and Biomedicine, among others, offering interested researchers a convenient reference guide to these latest advances.