Goal:
Understand Lipschitz continuity, the Bisection algoritm, the concepts
sequence, Cauchy sequence,
convergence and real number and the intermediate value theorem.
Reading:
AMBS chapt. 12-16.
Minimum reading: 12.2, 12.3, 12.8, 13.1, 13.5, 13.7, 13.9, 14.1-14.6,
15.1-15.5, 15.8, 16.1-16.2
Minimum reading: read only this during the first reading of the
book, later read the other parts too. If you have the lowest ambition
with the course you need only read the minimum.
Exercises:
13.1ac, 13.2, 13.3acd, 13.4ac, 13.5, 13.9, 13.10, 13.11, 13.14, 13.15, 13.16acfg, 13.19,
14.2a, 14.6ac, 14.7,
15.2, 15.3, (15.4,) 15.5, 15.6, 15.11, (15.13,) 15.14, 15.15, 15.17, 15.18, 15.19, 15.23, 15.24,
12.1, 12.3, 12.4, 12.5, 12.7, 12.9, 12.10, 12.11, 12.12, 12.14, 12.16, 12.17, 12.18, 12.19,
13.7, 13.8, 13.16bde, 13.17ac,
Project:
Project f(x)=0 , including
modeling, solver implementation, application to model equations,
analysis and conclusions, presentation.
Obs: Vi skippar detta projekt i år 2004! /stig
Goal:
A matlab function implementation of the Bisection algorithm (part of project work) for the solution of an arbitrary algebraic equation f(x)=0, with input arguments f, int and tol, where f is the name of a matlab function file defining y=f(x), int is a given interval containing a root, and tol is a given tolerance for the length of the final interval containing a root, and with output argument int, where int is the final interval containing the root.
Reading:
Recall from Matlab intro how to use while loops and conditional
code (if-elseif-else-end), and from the first ALA Matlab session about
how to write functions in Matlab. Also consult your Matlab Programming
book on these issues (chapters 3, 4 and 7).
Excercises:
13.21,
Här är Prov K och Prov
Kf/Bt.
G2: Work on problems in the book.
/stig