Prerequisite Materials for Math 162A
- Abstract Vector Space
Coodinate free definition of vectro space, function spaces, spaces of polynomials
- Inner product on vector space
Geometry introduced by the inner product, comparison of the inner product to the dot product
- Sigma notation and Einstein Convention
Einstein convention is the way to study n-dimensional "matrix" algebra.
- Invairiants of linear transformation
Linear algebra, by definiton, is the invariants theory of linear transformations
- Vector Calculus
Derivatives and partial derivatives of vector-valued or matrix-valued functions
- The Fundamental Theorem of ODE
Picard-Lindelöf Theorem, Implicit Function Theorem, etc