1. Newton's　method

  1. Introduction. Secant's method （Doc 1)
  2. One variable Newton's method. Convergence, choice of the initial value. （doc 2） (Mathematica: Tutorial and Linear Algebra)
  3. Generalization to systems of non-linear equations.(Mathematica: Tutorial 2 and Newton's method)
  4. Supplement： Approximation by Taylor expansions of implicit functions occuring i the Implicit Function Theorem. （ Doc 3）
    Quasi-Newton methods. Broyden's method.
    Bassin of attraction and Fractals

2. Inverting a matrix

  1. Direct methods：Gauss Elimination, error and pivot's selection (Doc ４）
  2. Iterative methods：Jacobi, Gauss-Seidel (Doc ５）、 （Doc ６）, (Mathematica's Problems）、 　(Review problems、Solution)
  3. Iterative methods 2: Descent's method, Conjugate Gradient method, (Summary+Problems)

３. Approximation of eigenvalues

  1. Power method
  2. Householder's transformation
  3. QR decomposition, (Summary＋Problems)