Linear Algebra Supplement to Calculus With Analytic Geometry
Linear algebra is the branch of mathematics concerning linear equations such as. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry , including for defining basic objects such as lines , planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models.
Notation can be unusual and awkward especially if the Einstein summation convention is used , definitions can be imprecise, and theorems may not always be supported by proof. Michael Spivak, in volume 5 of his five-volume magnum opus on differential geometry, once described the difficulties he had reading a derivation of the wave equation, and I remember thinking how elegantly he had described my own feelings on that subject:. There are lots of physics examples in this book including rotations, Minkowski spacetime and electromagnetism, Kepler motions and angular velocity but these enhanced the mathematical discussions rather than detracted from them. There were some occasional instances of strange terminology. But these were few, minor, and non-disruptive. The first six chapters concern basic sophomore-level linear algebra.
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