Theory

Goal:
Understand Lipschitz continuity, the Bisection algoritm, the concepts sequence, Cauchy sequence, convergence and real number and the intermediate value theorem.

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

Matlab

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.

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,

Activity plan:

L=Lecture, S=Studio, G=Group work
L1: Lipschitz continuity, sequences, convergence (AMBS ch. 12-13).
S1: The Bisection Algorithm
G1: Work on problems from the book.
S2: Continue with session A3 (K students will not have this lesson).
L2: The Bisection algorithm, Cauchy sequence, real number. Chapter 14-15.
L3: More on convergence, Lipschitz continuity, and the question if the equation really got solved, Bolzano's theorem and The Intermediate Value Theorem. Chapter 15-16.
S3: Diagnostic test in Matlab programming.
Detta är ett diagnostiskt prov på matlabkunskap. Det kommer inte att påverka ditt betyg på kursen utan det avser att ge oss lärare information om hur vi lyckats med undervisningen och ge dig information om hur du ligger till och vad vi kräver av dig. Den som blir underkänd idag behöver inte göra något nytt prov utan får ta på sitt eget ansvar att (med lärarnas hjälp) komma ikapp.

Här är Prov K och Prov Kf/Bt.

G2: Work on problems in the book.

/stig