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Applied Linear Algebra (2nd Edition)

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Publisher:

Springer

Pages: 679
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Hardcover - 9783319910406

30 May 2018

€64.19

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Ebook - 9783319910413

30 May 2018

€51.16

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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...

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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.

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Develops a strong conceptual grounding for applying linear algebra in numerous modern applications


Weaves the theory of linear algebra with applications across engineering, science, computing, data analysis, and beyond

Provides an ideal preparation for future study in applied differential equations

Presents material in engaging and informative full color

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.
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Peter Olver is Professor of Mathematics at University of Minnesota, Twin Cities. His research centers around Lie groups, differential equations, and various areas of applied mathematics. His previous books include Introduction to Partial Differential Equations (Springer, UTM, 2014), and Applications of Lie Groups to Differential Equations (Springer, GTM 107, 1993).

Chehrzad Shakiban is Professor of Mathematics at University of St. Thomas, St. Paul. Her interests include calculus of variations, computer vision, and innovative learning experiences that illustrate connections between mathematics and the arts.

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Peter Olver is Professor of Mathematics at University of Minnesota, Twin Cities. His research centers around Lie groups, differential equations, and various areas of applied mathematics. His previous books include Introduction to Partial Differential Equations (Springer, UTM, 2014), and Applications of Lie Groups to Differential Equations (Springer, GTM 107, 1993).

Chehrzad Shakiban is Professor of Mathematics at University of St. Thomas, St. Paul. Her interests include calculus of variations, computer vision, and innovative learning experiences that illustrate connections between mathematics and the arts.

Show Less

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