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 Schrodinger 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 Infinite-dimensional 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.

nexusstc/Applied Linear Algebra: The Decoupling Principle/d428d0cb0534c918bb2daa7f9e24d0dc.djvu

lgli/Sadun L. Applied linear algebra. The decoupling principle (2ed., mbk-50, AMS, 2008)(ISBN 9780821844410)(600dpi)(T)(391s)_MAl_.djvu

lgrsnf/Sadun L. Applied linear algebra. The decoupling principle (2ed., mbk-50, AMS, 2008)(ISBN 9780821844410)(600dpi)(T)(391s)_MAl_.djvu

2nd ed., Providence, R.I, Rhode Island, 2008

United States, United States of America

2nd ed, Providence, cop. 2008

lg2710820

{"edition":"2","isbns":["0821844415","9780821844410"],"last_page":371,"publisher":"American Mathematical Society"}

Includes index.

Writing for junior and senior undergraduates, Sadun (mathematics, U. of Texas at Austin) offers diagonalization (reducing coupled linear evolution problems to a sequence of simpler decoupled problems) as a significant tool suitable for physics and engineering as well as in mathematics. He explains vector spaces and bases, linear transformations and operators, eigenvalues, circles and ellipses, inner products, adjoints, Hermitian operators, unitary operators, the wave equation, continuous spectre and the Dirac delta function, Fourier transforms, Green's and functions, and includes an appendix on matrix operations (new to this edition) and a full chapter on crucial applications. For this edition he also includes new exercises (with solutions), and a series of very good numerical labs, some of which are theoretical and relate linear algebra to quantum physics. Sadun also thoughtfully supplies a section for instructors, including recommendations for course outlines. Annotation 2008 Book News, Inc., Portland, OR (booknews.com)

"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." "Sadun includes some topics relating to infinite-dimensional 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."--Jacket

2020-07-27