# Schedule

This schedule is not yet final. Changes will be made during the semester. At the end of the course this page will constitute the curriculum of TMA4215.

CK = Cheney and Kincaid, Numerical Analysis

N = Notes

Week Date CK N Subject Links
34 26.08, 27.08 Ch. 1 Ch. 2 Ch. 4.4 Background. Floatingpoint numbers, rounding errors, stability of problems and algorithms. Condition numbers. Floating point numbers. Interval arithmetic. Computer assisted proofs. Taylor's theorem. Big O notation.
35 02.09, 03.09 Ch.1.1 and 1.2 Ch. 4.4. Ch. 3.0, 3.1, 3.2, 3.3 Taylor's theorem and Big O notation. Condition number for linear systems. Numerical solution of nonlinear equations. Cramer's rule.
36 09.09, 10.09 Ch. 3.4, 4.0 4.1. Nonlinear systems of equations. Note about nonlinear equations. You should read ch 4.0, 4.1 on your own.
37 16.09, 17.09 Ch. 4.2, 4.3, 4.5, 5.2. LU- Cholesky and other factorizations. The Neumann series. In 5.2 only Gershgoring's theorem. Note on linear algebra with some examples (with small matrices).
38 23.09, 24.09 Ch. 6.1 Interpolation. Lagrange interpolation polynomial. Chebishev points and optimality of the interpolation error.
39 30.09, 01.10 Supervision of the first project.
40 07.10, 08.10 Ch. 6.2. Divided differences and Newton form of the interpolation polynomial. Matlab codes interpolation.m and lk.m. Can be used for comparison of interpolation on equidistant and Chebyshev nodes.
41 14.10, 15.10 Ch. 6.3, 6.4 (theorem 1 included), 7.1. Hermite interpolation, splines, numerical differentiation. der.pdf Error in the numerical approximation of the derivative of cos(x) for x=3,(-sin(3)=-0.14112000805987), by difference approximations (Taylor theorem) and for smaller and smaller values of h. When h is too small the rounding error starts propagating.
42 21.10, 22.10 Ch. 7.1, 7.2, 7.4 Numerical differentiation, quadrature, Romberg algorithm. Note on Euler-Mclaurin formula and Bernoulli polynomials.
43 28.10, 29.10 Ch. 7.3, 7.5, 8 Gauss quadrature and Adaptive quadrature. Note on orthogonal polynomials. Note on odes, introduction.
44 04.11, 05.11 Ch. odesNote on odes, Euler method, convergence. Runge-Kutta methods. Implementation of explicit and implicit Euler. Checking the order of a method.
45 11.11, 12.11 Ch. odes RK-methods order conditions. Supervision of the second project.
46 18.11, 19.11 Ch. odes RK-methods step-size selection and linear stability. Linear multi-step methods.
47 25.11, 26.11 Ch. odes