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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. 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. Her interests include calculus of variations, computer vision, and innovative learning experiences that illustrate connections between mathematics and the arts.
Download PDF by Peter J. Olver, Cheri Shakiban: Applied Linear Algebra - Instructor Solutions Manual. Chehrzad Shakiban. Department of. Linear algebra is motivated by the need to solve systems of linear algebraic equations in a finite. These classical linear algebra topics are of much less importance in applied mathematics, in contrast to.
This work is protected by local and international copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from this site should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. For in-depth Linear Algebra courses that focus on applications. This text aims to teach basic methods and algorithms used in modern, real problems that are likely to be encountered by engineering and science students—and to foster understanding of why mathematical techniques work and how they can be derived from first principles.
No text goes as far (and wide) in applications. The authors present applications hand in hand with theory, leading students through the reasoning that leads to the important results, and provide theorems and proofs where needed. Because no previous exposure to linear algebra is assumed, the text can be used for a motivated entry-level class as well as advanced undergraduate and beginning graduate engineering/applied math students.
Features. Abundant exercises—Appear after almost every subsection, in a wide range of difficulty. Starts each exercise set with straightforward computational problems to test and reinforce the new techniques and ideas.
Presents more advanced and more theoretical exercises later on in the set. Includes numerous computer-based exercises and in-depth projects.
Discussion of the basics of matrices, vectors, and Gaussian elimination. Coverage of less-familiar topics from linear systems theory—Includes the LU decomposition and its permuted versions. Wide range of illustrative examples to explain essential concepts of vector space, subspace, span, linear independence, basis, and dimension—Addresses the difficulty students often have with these concepts. Concurrent development of the finite-dimensional and function space cases in Chapters 2 and 3 (Inner Products and Norms). An entire chapter (Chapter 6) devoted to applications of the concepts of Minimization and Least Squares and Orthogonality.
Flexible presentation of Linear Functions, Linear Transformations, and Linear Systems (Chapter 7)—Can be covered or omitted as desired. Coverage of eigenvalues and their applications in linear dynamical systems governed by ordinary differential equations and iterative systems, such as Markov chains and numerical solution algorithms. Complete discussions of numerical linear algebra, including pivoting strategies, condition numbers, iterative solution methods such as Gauss- Seidel and SOR, singular value decomposition, the QR algorithm, and finite elements. Unique chapter on Boundary Value Problems in One Dimension (Chapter 11).
Presents topics from applied linear analysis such as delta functions, Green's function, and finite elements, as a completely natural development of linear algebra in function spaces. Text-specific website at a number of illustrative MATLAB problems the authors used in teaching the course.
Reviews Some Quotes from Reviewers “The material on the concept of a general vector space, linear independence, basis, etc. Is always difficult for students in this course. This book handles it very well. It gives full, clear explanations. The style is very good, clear, and thorough. It should appeal to my students.
I like the book very much. It subscribes to the same philosophy of linear algebra as pioneered by Strang some 30 years ago (acknowledged in the introduction) and builds on the Strang books, making things even clearer and adding more topics. I would certainly like to use this book and would recommend it to my colleagues.” -Bruno Harris, Brown University “I like the book very much. We will consider it for our linear algebra courses. This is the best new book to appear since the text by Gilbert Strang. It is really modern book, combining, in a masterful, core and applied aspects of linear algebra. This is a very good book written by a very good mathematician and a very good teacher.” -Juan J.
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Manfredi, University of Pittsburgh “In many, if not most, beginning texts of linear algebra, the applications may be collected together in a chapter at the end of the book or in an appendix, leaving any inclusion of this material to the discretion of the instructor. However, Applied Linear Algebra by Olver and Shakiban completely reverses this procedure with a total integration of the application with the abstract theory.
The effect on the reader is quite amazing. The reader slowly begins to realize two main points: (1) how applications generally drive the abstract theory, and (2) how the abstract theory can illuminate the applications, and resolve solutions in very striking ways. This text is easily the best beginning linear algebra text dealing with the applications in an integrated way that I have seen. There is no doubt that this text will be the standard to which all beginning linear algebra texts will be compared. Simply put, this is an absolutely wonderful text!” -Norman Johnson, University of Iowa “I lover the style of this book, especially the fact that you could feel the authors’ enthusiasm about the nice mathematics involved in the theory. The examples were very clear and interesting, and they always tried to approach the same problems over and over again as soon sas they had more weapons at their disposal to attack them.
I thought this was great, this text introduces the notion of an abstract space very early (still, after Gaussian Elimination) and in a very natural way, then emphasizes along the way over and over again that tremendously. I would absolutely consider this text. I was really taken by the applications and the organization of the materials. I also loved the abundance of exercises and problems.” -Tamas Wiandt, Rochester Institute of Technology “This text is very well-written, has lots of examples, and is easy to read and learn from.
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I’d use it in my Matrix Methods class. There is a good mixture of routine and more advanced examples.” -James Curry, University of Colorado-Boulder “I believe the writing style would appeal to my students because of the clarity and the examples, as well as the tone. I am going to consider its use, once I see its final form.” -Fabio Augusto Miner, Purdue University. Other student resources. Student Solutions Manual for Applied Linear Algebra Olver & Shakiban ISBN-10:.
ISBN-13: 843 ©2005. Paper, 184 pp. Available on Demand? IsFirstMoreInfoLinkRendered=false isSecondMoreInfoLinkRendered=false caseVariable=false chkOnlineProduct=false chkCategoryInList=false chkCategoryNotInList=true answerBookRest= path/ProductBean/statusCode=8 productCategory=11 path/ProductBean/uopsTitleStatCd= productPrice=34.99 tabId=SR isBuyable=true /Properties/Data/Result/PearsonRoot/ProductBean/sourceCode=UK. Pearson Learning Solutions Nobody is smarter than you when it comes to reaching your students. You know how to convey knowledge in a way that is relevant and relatable to your class. It's the reason you always get the best out of them.
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