Weekly plan for Math 417-500 (approximate)

  • Week 1. Review of calculus, roundoff errors.
    Sections 1.1-1.2

  • Week 2. The bisection method and fixed point iteration.
    Sections 2.1-2.2

  • Week 3. Newton's method and error analysis.
    Sections 2.3-2.4

  • Week 4. Aitken's method, linear systems of equations.
    Sections 2.5,6.1

  • Week 5. Gaussian Elimination with partial pivoting, Test 1.
    Sections 6.2

  • Week 6. Linear algebra and matrix inversion, matrix factorization
    Sections 6.3-6.5.

  • Week 7. Special matrices, Lagrange interpolation
    Section 6.6,3.1.

  • Week 8. Divided differences, Hermite interpolation.
    Section 3.2,3.3.

  • Week 9. Cubic Spline interpolation, Test 2.
    Sections 3.4

  • Week 10. Numerical differentiation, Richardson Extrapolation
    Sections 4.1,4.2.

  • Week 11. Numerical integration, composite numerical integration, multiple integrals.
    Section 4.3,4.4,4.8.

  • Week 12. Gaussian quadrature.
    Section 4.7.

  • Week 13. Review of initial value problems, Taylor methods.
    Section 5.1-5.3.

  • Week 14. Runge-Kutta and multistep methods.
    Section 5.4,5.6