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Applied Linear Algebra By Peter J. Olver

Applied Linear Algebra by Peter J. Olver

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Applied Linear Algebra Summary

Applied Linear Algebra by Peter J. Olver

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.

About Peter J. Olver

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.

Table of Contents

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.

Additional information

GOR011487146
9783319910406
331991040X
Applied Linear Algebra by Peter J. Olver
Used - Like New
Hardback
Springer International Publishing AG
2018-06-14
679
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
The book has been read, but looks new. The book cover has no visible wear, and the dust jacket is included if applicable. No missing or damaged pages, no tears, possible very minimal creasing, no underlining or highlighting of text, and no writing in the margins

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