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Applied linear algebra

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Applied linear algebra/ by Peter J. Olver, Chehrzad Shakiban.
作者:	Olver, Peter J.
其他作者:	Shakiban, Chehrzad.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xxv, 679 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Mathematics. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-91041-3
ISBN:	9783319910413

Applied linear algebra
Olver, Peter J.

Applied linear algebra[electronic resource] /by Peter J. Olver, Chehrzad Shakiban. - 2nd ed. - Cham :Springer International Publishing :2018. - xxv, 679 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,0172-6056. - Undergraduate texts in mathematics..

Preface -- 1. Linear Algebraic Systems -- 2. Vector Spaces and Bases -- 3. Inner Products and Norms -- 4. Minimization and Least Squares Approximation -- 5. Orthogonality -- 6. Equilibrium -- 7. Linearity -- 8. Eigenvalues -- 9. Linear Dynamical Systems -- 10. Iteration of Linear Systems -- 11. Boundary Value Problems in One Dimension -- References -- Index.

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.

ISBN: 9783319910413

Standard No.: 10.1007/978-3-319-91041-3doiSubjects--Topical Terms:

527692
Mathematics.

LC Class. No.: QA184.2 / .O48 2018

Dewey Class. No.: 512.5

Applied linear algebra
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520 $a 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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