Overview
- Visit here for updated student and instructor solutions https://www-users.cse.umn.edu/~olver/ala.html
- 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 engaging and full color preparation for future study in applied differential equations
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (10 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Applied Linear Algebra
Authors: Peter J. Olver, Chehrzad Shakiban
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-91041-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-91040-6Published: 14 June 2018
Softcover ISBN: 978-3-030-08160-7Published: 10 January 2019
eBook ISBN: 978-3-319-91041-3Published: 30 May 2018
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 2
Number of Pages: XXV, 679
Number of Illustrations: 42 b/w illustrations, 88 illustrations in colour
Topics: Linear and Multilinear Algebras, Matrix Theory, Mathematical Applications in the Physical Sciences