Application-inspired linear algebra / Heather A. Moon, Thomas J. Asaki, Marie A. Snipes.
2022
QA184.2
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Details
Title
Application-inspired linear algebra / Heather A. Moon, Thomas J. Asaki, Marie A. Snipes.
Author
Moon, Heather A., author.
ISBN
9783030861551 (electronic bk.)
3030861554 (electronic bk.)
9783030861544
3030861546
3030861554 (electronic bk.)
9783030861544
3030861546
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource : illustrations (some color).
Item Number
10.1007/978-3-030-86155-1 doi
Call Number
QA184.2
Dewey Decimal Classification
512/.5
Summary
This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, one of which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.
Note
Includes index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Springer undergraduate texts in mathematics and technology.
Available in Other Form
Application-inspired linear algebra.
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Table of Contents
1 Introduction
2 Vector Spaces
3 Vector Space Arithmetic and Representations
4 Linear Transformations
5 Invertibility
6 Diagonalization
7 Inner Product Spaces and Pseudo-Invertibility
8 Conclusions
A Radiography and Tomography
B The Diffusion Equation
C Proof Techniques
D Fields.
2 Vector Spaces
3 Vector Space Arithmetic and Representations
4 Linear Transformations
5 Invertibility
6 Diagonalization
7 Inner Product Spaces and Pseudo-Invertibility
8 Conclusions
A Radiography and Tomography
B The Diffusion Equation
C Proof Techniques
D Fields.