Prerequisite Materials for Math 162A
  1. Abstract Vector Space
    Coodinate free definition of vectro space, function spaces, spaces of polynomials

  2. Inner product on vector space
    Geometry introduced by the inner product, comparison of the inner product to the dot product

  3. Sigma notation and Einstein Convention
    Einstein convention is the way to study n-dimensional "matrix" algebra.

  4. Invairiants of linear transformation
    Linear algebra, by definiton, is the invariants theory of linear transformations

  5. Vector Calculus
    Derivatives and partial derivatives of vector-valued or matrix-valued functions

  6. The Fundamental Theorem of ODE
    Picard-Lindelöf Theorem, Implicit Function Theorem, etc

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