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Book Details2008; 371 ppMSC: Primary 15; Secondary 34; 35; 39; 42;
Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle.
Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrödinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings.
Sadun includes some topics relating to infinitedimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform.
The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.ReadershipUndergraduate students interested in linear algebra; applications of linear algebra.

Table of Contents

Chapters

1. The decoupling principle

2. Vector spaces and bases

3. Linear transformations and operators

4. An introduction to eigenvalues

5. Some crucial applications

6. Inner products

7. Adjoints, Hermitian operators, and unitary operators

8. The wave equation

9. Continuous spectra and the Dirac delta function

10. Fourier transforms

11. Green’s functions

12. Matrix operations

13. Solutions to selected exercises


Additional Material

Reviews

Sadun's writing style [is] very natural and straightforward. The book has a large number of exercises, ranging from the computational to the theoretical. ...For all these reasons, I can imagine using Sadun's books in a number of different ways. The author's exposition is so clear and littered with examples and motivation for the material that I would not hesitate to point a student wishing to do an independent study to this book. If we were to teach a second semester of linear algebra, I would certainly consider this book to be a frontrunner as a choice of texts. As it is, I will keep this book on my desk next time I teach our existing linear algebra course, as a source of examples, problems, and ideas for my own teaching.
MAA Reviews 
This is a book which can be recommended to anyone interested in the mathematical foundation of principles and techniques used in many applications of Linear Algebra to the real world.
Monatshafte für Mathematik


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 Book Details
 Table of Contents
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Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle.
Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrödinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings.
Sadun includes some topics relating to infinitedimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform.
The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
Undergraduate students interested in linear algebra; applications of linear algebra.

Chapters

1. The decoupling principle

2. Vector spaces and bases

3. Linear transformations and operators

4. An introduction to eigenvalues

5. Some crucial applications

6. Inner products

7. Adjoints, Hermitian operators, and unitary operators

8. The wave equation

9. Continuous spectra and the Dirac delta function

10. Fourier transforms

11. Green’s functions

12. Matrix operations

13. Solutions to selected exercises

Sadun's writing style [is] very natural and straightforward. The book has a large number of exercises, ranging from the computational to the theoretical. ...For all these reasons, I can imagine using Sadun's books in a number of different ways. The author's exposition is so clear and littered with examples and motivation for the material that I would not hesitate to point a student wishing to do an independent study to this book. If we were to teach a second semester of linear algebra, I would certainly consider this book to be a frontrunner as a choice of texts. As it is, I will keep this book on my desk next time I teach our existing linear algebra course, as a source of examples, problems, and ideas for my own teaching.
MAA Reviews 
This is a book which can be recommended to anyone interested in the mathematical foundation of principles and techniques used in many applications of Linear Algebra to the real world.
Monatshafte für Mathematik