Applied Linear Algebra -2/E

Peter J. Olver, Chehrzad Shakiban

Informasi Dasar

20.21.514
512
Buku - Elektronik (E-Book)
10a

Applied mathematics rests on two central pillars: calculus and linear algebra. While calculus has its roots in the universal laws of Newtonian physics, linear algebra arises from a much more mundane issue: the need to solve simple systems of linear algebraic equations. Despite its humble origins, linear algebra ends up playing a comparably profound role in both applied and theoretical mathematics, as well as in all of science and engineering, including computer science, data analysis and machine learning, imaging and signal processing, probability and statistics, economics, numerical analysis, mathematical biology, and many other disciplines. Nowadays, a proper grounding in both calculus and linear algebra is an essential prerequisite for a successful career in science, technology, engineering, statistics, data science, and, of course, mathematics. Since Newton, and, to an even greater extent following Einstein, modern science has been confronted with the inherent nonlinearity of the macroscopic universe. But most of our insight and progress is based on linear approximations. Moreover, at the atomic level, quantum mechanics remains an inherently linear theory. (The complete reconciliation of linear quantum theory with the nonlinear relativistic universe remains the holy grail of modern physics.) Only with the advent of large-scale computers have we been able to begin to investigate the full complexity of natural phenomena. But computers rely on numerical algorithms, and these in turn require manipulating and solving systems of algebraic equations. Now, rather than just a handful of equations, we may be confronted by gigantic systems containing thousands (or even millions) of unknowns. Without the discipline of linear algebra to formulate systematic, efficient solution algorithms, as well as the consequent insight into how to proceed when the numerical solution is insufficiently accurate, we would be unable to make progress in the linear regime, let alone make sense of the truly nonlinear physical universe.

Subjek

ALGEBRA
 

Katalog

Applied Linear Algebra -2/E
978-3-319-910 41-3
679p.; il.; 8.9 MB
English

Sirkulasi

Rp. 0
Rp. 0
Tidak

Pengarang

Peter J. Olver, Chehrzad Shakiban
Perorangan
-
-

Penerbit

Springer
New York
2018

Koleksi

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  • CII9B3 - SAINS DATA LANJUT
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