Rough weekly schedule for M450

  • Week 1
    Section 1.1 Basic concepts and Taylor's Theorem
    Section 1.2 Order of convergence, Big O notation
    Section 2.1 Floating point arithmetics

  • Week 2
    Section 2.2 Absolute and relative errors
    Section 2.3 Stability and conditioning

  • Week 3
    Section 3.1 Bisection method
    Section 3.2 Newton's method

  • Week 4
    Section 3.3 Secant method
    Section 3.4 Fixed point iteration

  • Week 5
    Section 3.2 Newton's method for systems
    Section 3.5 Computing zeros of polynomials

  • Week 6
    Section 4.1 + "Crash course in linear algebra"

  • Week 7
    Section 4.2 LU and Cholesky decompositions
    Section 4.3 Gaussian elimination

  • Week 8
    Section 4.3 Pivoting and constructing an algorithm
    Section 4.3 Operation counts
    Section 4.4 Norms and analysis of errors

  • Week 9
    Section 4.5 Neumann series and iterative refinement
    Section 4.6 Jacobian iteration

  • Week 10
    Section 4.6 Gauss-Seidel iteration
    Section 4.6 SOR iteration
    Conjugate Gradient (handout)

  • Week 11
    Section 6.1 Polynomial interpolation
    Section 6.2 Divided differences

  • Week 12
    Section 6.2 Divided differences
    Section 6.3 Hermite interpolation
    Section 6.4 Splines

  • Week 13
    Section 6.5 B-Splines - basic theory
    Section 6.6 B-SPlines - applications

  • Week 14
    Section 6.8 Best approximation - least squares
    Section 6.9 Best approximation - Chebyshev theory

  • Week 15
    Section 7.1 Numerical differentiation
    Section 7.2 Newton-Cotes rules
    Section 7.3 Gaussian quadrature
    Section 7.5 Adaptive quadrature