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Author: Heather A. Moon
Publisher: Springer Nature
ISBN: 3030861554
Category : Mathematics
Languages : en
Pages : 539
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Book Description
This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, one of which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors’ website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.
Author: Heather A. Moon
Publisher: Springer Nature
ISBN: 3030861554
Category : Mathematics
Languages : en
Pages : 539
Get Book
Book Description
This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, one of which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors’ website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.
Author: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477
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Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: Howard Anton
Publisher: John Wiley & Sons
ISBN: 0470432055
Category : Mathematics
Languages : en
Pages : 786
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Book Description
Elementary Linear Algebra 10th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. Technology also is not required, but for those who would like to use MATLAB, Maple, or Mathematica, or calculators with linear algebra capabilities, exercises are included at the ends of chapters that allow for further exploration using those tools.
Author: Ward Cheney
Publisher: Jones & Bartlett Publishers
ISBN: 1449613527
Category : Mathematics
Languages : en
Pages : 649
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Book Description
Ward Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multi-faceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For theoretically-oriented students, the text guides them as they devise proofs and deal with abstractions by focusing on a comprehensive blend between theory and applications. For application-oriented science and engineering students, it contains numerous exercises that help them focus on understanding and learning not only vector spaces, matrices, and linear transformations, but uses of software tools available for use in applied linear algebra. Using a flexible design, it is an ideal textbook for instructors who wish to make their own choice regarding what material to emphasis, and to accentuate those choices with homework assignments from a large variety of exercises, both in the text and online.
Author: Jim DeFranza
Publisher: Waveland Press
ISBN: 1478628820
Category : Mathematics
Languages : en
Pages : 508
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Book Description
Over the last few decades, linear algebra has become more relevant than ever. Applications have increased not only in quantity but also in diversity, with linear systems being used to solve problems in chemistry, engineering, economics, nutrition, urban planning, and more. DeFranza and Gagliardi introduce students to the topic in a clear, engaging, and easy-to-follow manner. Topics are developed fully before moving on to the next through a series of natural connections. The result is a solid introduction to linear algebra for undergraduates’ first course.
Author: Howard Anton
Publisher: John Wiley & Sons
ISBN: 9788126518692
Category : Algebras, Linear
Languages : en
Pages : 856
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Book Description
Market_Desc: · Engineers· Mathematicians· Math students Special Features: · Clear, accessible, step-by-step explanations make the material crystal clear. The authors spotlight the relationships between concepts to give a unified and complete picture.· Establishes the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigen values. About The Book: This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.
Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 0817643702
Category : Mathematics
Languages : en
Pages : 202
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Book Description
* Proposes a radically new and thoroughly algorithmic approach to linear algebra * Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples * Designed for a one-semester course, this text gives the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject
Author: Peter J. Olver
Publisher: Springer
ISBN: 3319910418
Category : Mathematics
Languages : en
Pages : 679
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Book Description
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.
Author: Edgar G Goodaire
Publisher: World Scientific Publishing Company
ISBN: 981450839X
Category : Mathematics
Languages : en
Pages : 732
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Book Description
This is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it also includes more advanced topics such as the pseudoinverse and the singular value decomposition that make it appropriate for a more advanced course as well. As is becoming increasingly the norm, the book begins with the geometry of Euclidean 3-space so that important concepts like linear combination, linear independence and span can be introduced early and in a “real” context. The book reflects the author's background as a pure mathematician — all the major definitions and theorems of basic linear algebra are covered rigorously — but the restriction of vector spaces to Euclidean n-space and linear transformations to matrices, for the most part, and the continual emphasis on the system Ax=b, make the book less abstract and more attractive to the students of today than some others. As the subtitle suggests, however, applications play an important role too. Coding theory and least squares are recurring themes. Other applications include electric circuits, Markov chains, quadratic forms and conic sections, facial recognition and computer graphics.
Author: Milan Vujicic
Publisher: Springer Science & Business Media
ISBN: 3540746390
Category : Science
Languages : en
Pages : 294
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Book Description
The author of this book was Professor of Theoretical Physics at the University of Belgrade. The book is based on lectures he gave there to both undergraduate and postgraduate students over a period of several decades. It sets out to explain Linear Algebra from its fundamentals to the most advanced level. A special feature of this book is its didactical approach, with a myriad of thoroughly worked examples and excellent illustrations, which allows the reader to approach the subject from any level and to proceed to that of the most advanced applications. Throughout, the subject is explained with painstaking care.
