Applied linear algebra / Peter J. Olver, Chehrzad Shakiban

By: Olver, Peter J [author]Contributor(s): Shakiban, Chehrzad, 1951- [author] | Ohio Library and Information NetworkMaterial type: TextTextSeries: Undergraduate texts in mathematicsPublisher: Cham : Springer, 2018Edition: Second editionDescription: 1 online resource (xxv, 679 pages) : illustrations (partly color)Content type: text Media type: computer Carrier type: online resourceISBN: 3319910418; 9783319910413Subject(s): Algebras, Linear | MathematicsGenre/Form: Electronic books Additional physical formats: Printed edition:: No titleDDC classification: 512/.5 LOC classification: QA184.2 | .O48 2018Online resources: SpringerLink Connect to resource | SpringerLink Connect to resource | SpringerLink Connect to resource (off-campus)
Contents:
1. Linear algebraic systems -- 2. Vector spaces and bases -- 3. Inner products and norms -- 4. Orthogonality -- 5. Minimization and least squares -- 6. Equilibrium -- 7. Linearity -- 8. Eigenvalues and singular values -- 9. Iteration -- 10. Dynamics
Summary: 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
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e-Books e-Books Main Library -University of Zimbabwe
Click on Online resources to access the e-Book QA184.2 .O48 2018 (Browse shelf (Opens below)) Available

Includes bibliographical references and indexes

1. Linear algebraic systems -- 2. Vector spaces and bases -- 3. Inner products and norms -- 4. Orthogonality -- 5. Minimization and least squares -- 6. Equilibrium -- 7. Linearity -- 8. Eigenvalues and singular values -- 9. Iteration -- 10. Dynamics

Available to OhioLINK libraries

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

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