Application-Inspired Linear Algebra

This textbook presents abstract linear algebra concepts through real-world applications like diffusion welding and radiography. It encourages students to learn through explorations, making conjectures, and answering open-ended questions. The book covers vector spaces, eigenvalues, data and image analysis, dynamical modeling, and optimization and optimal design, with appendices and an instructor's outline. Additional resources are available on the authors' website.

Format: Hardback
Length: 528 pages
Publication date: 21 May 2022
Publisher: Springer Nature Switzerland AG

This comprehensive textbook offers an engaging and accessible introduction to abstract ideas in linear algebra, seamlessly integrating them within the context of practical applications. The two central applications, diffusion welding and radiography, are introduced early on and serve as a framework for understanding the practical uses of essential linear algebra concepts. Through a series of explorations, students engage in making conjectures and answering open-ended questions, fostering a deep understanding of the subject matter. By approaching linear algebra in this innovative way, new avenues for learning emerge. For instance, vector spaces are introduced as the appropriate setting for the applied problems covered, while an alternative, determinant-free method for computing eigenvalues is also demonstrated.

In addition to the two main applications, the authors provide insightful descriptions of potential pathways to other applications, which fall into three main areas: data and image analysis (including machine learning), dynamical modeling, and optimization and optimal design. Numerous appendices are included, one of which offers an insightful walkthrough of proof techniques. Instructors will find an outline for effectively utilizing the book in a course, along with additional resources accessible on the authors' website, including code, data sets, and other valuable materials.

Application-Inspired Linear Algebra is designed to captivate and engage undergraduate students embarking on their first course in linear algebra, while also providing instructors with a valuable and application-focused approach. By presenting linear algebra through real-world scenarios and fostering a hands-on learning experience, this textbook equips students with the skills and knowledge necessary to excel in various fields and pursue their academic and professional aspirations.

Weight: 1258g
Dimension: 183 x 260 x 36 (mm)
ISBN-13: 9783030861544
Edition number: 1st ed. 2022