Course contents:

Projects: Form a matrix from Laplacian

Preliminary:
(Some motivation before going into matrix problem and nonlinear)
also eig
borrow mins slides of qdot
the 2D Laplacian


Chap 0: Programming Language Tutorial.
  0.1: Matlab (Octave) Tutorial

Chap 1: Mathematical Preliminaries and Error Analysis  (21)
  1.2: Rounding Errors and Computer Arithmetic     (13)
  1.3: Algorithms and Convergence                  ( 8)

Chap 2: Solutions of Equations in One Variable         (51)
  2.1: Bisection                                   ( 7)
  2.2: Fixed Point Iteration                       (10)
  2.3: Newton's method                             (12)
  2.4: Error Analysis for Iterative Methods        ( 8)
  2.5: Accelerating Convergence                    ( 4)
  2.6: Muller's Method                             (10)

Chap 3: Interpolation and polynomial approximation     (53)
  3.1: Interpolation and Lagrangian polynomial     (15)
  3.2: Divided Difference                          (11)
  3.3: Hermite Interpolation                       ( 7)
  3.4: Cubic Spline Interpolation                  (20)

Chap 4: Numerical differentiation and integration      (45)
  4.1: Numerical Differentiation                   (11)
  4.2: Richardson Extrapolation                    ( 8)
  4.3: Elements of Numerical Integration           ( 9)
  4.4: Composite Numerical Integration             (11)
% 4.5: Romberg Integration                         ( 5)
% 4.6: Adaptive Quadrature                         ( 8)
  4.7: Gaussian Quadrature                         ( 6)
% 4.8: Multiple Integrals                          (15)
  4.9: Improper Integrals                          ( 5)

Chap 6: Direct Methods for Solving Linear Systems      (49)
  6.1: Linear System of Equations                  (14)
  6.2: Pivoting Strategies                         (10)
  6.5: Matrix Factorization                        (10)
  6.6: Special Types of Matrices                   (15)

Chap 07: Iterative Techniques in Matrix Algebra                   (61)
    7.1: Norms of vectors and matrices                         (11)
    7.2: Eigenvalues and eigenvectors                          ( 7)
    7.3: Iterative techniques for solving linear systems       (18)
    7.4: Error bounds and iterative refinement                 (10)
    7.5: The conjugate gradient method                         (15)

Chap 08: Approximation Theory                                           (62)
    8.1: Discrete least square approximation                      (12)
    8.2: Orthogonal polynomial and least square approximation     ( 9)
    8.3: Chebyshev polynomials and economization of power series  ( 9)
    8.4: Rational function approximation                          (11)
    8.5: Trigonometric polynomial approximation                   ( 9)
    8.6: Fast Fourier Transforms                                  (12)

Chap 09: Approximating Eigenvalues                     (26) 
    9.1: Linear algebra and eigenvalues            ( 9)
    9.2: The power method                          (17)

Chap 10: Numerical Solutions of Nonlinear Systems of Equations     (33+8)
   10.1: Fixed points for functions of several variables        ( 9)
   10.2: Newton's method                                        (10)
   10.3: Quasi-Newton methods                                   ( 7)
   10.4: Steepest Descent Techniques                            ( 7)
%  10.5: Homotopy and continuation methods                      ( 8)

Chap 5: IVP for ODE                                    (17)
   5.2: Euler's Method                             (10)  
   5.3: Higher-Order Taylor Methods                ( 7)