Applied Linear Algebra: The Decoupling Principle - Brossura

Sadun, Lorenzo

Brossura

ISBN 10: 1470470047 ISBN 13: 9781470470043

Casa editrice: Amer Mathematical Society, 2008

Riassunto

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.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 1470470047
• ISBN 13: 9781470470043
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 371
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile