Matematik och Datavetenskap, Chalmers Tekniska Högskola och Göteborgs Universitet
Each student must keep an individual folder (pärm) containing documentation of the obligatory work. The folder must be handed in at the exam. Each student must also keep a copy of each obligatory program that we write. These programs may be used in future courses.
At least some of the documentation should be written with a word processing program such as ms-word or latex. (Many of us have lousy handwriting and that is simply not acceptable in a professional report. But I accept that it may be too time consuming to do all of it on the computer in the beginning. ) See Johan Hoffman's presentation manual.
The purpose of the folder is:
a) each student should write and keep certain matlab programs for future use;
b) each student should write down some mathematics every week (writing down your work forces you to reflect about what you have done and you will learn better);
c) some basic mathematical topics are emphasized. These basic topics must be mastered by every student. About half of the exam questions will therefore be taken directly from the obligatory topics.
Week 1.
The fundamental theorem of calculus.
Write down the proof of The Fundamental
Theorem of Calculus and put it in your individual folder. Emphasize
the following steps:
1. construction of Un.
2. proof that Un is a Cauchy sequence.
3. proof that u(x) satisfies the differential
equation.
4. u is unique.
This proof is an important part of the
course and you must understand it well. Then the later parts of the
course will be much easier. The program my_int.m.
Week 2. How small is the error?
Week 3. My ode solver 1.
Week 4. None.
Week 5.
92. Analytical computation of integrals
(postscript).
93. Analytical solution of differential
equations
(postscript), problems 93.1 - 93.10.
Week 6.
90.1, 2, 3, 4, 5, 6 from
90. Linearization and Newton's method.
(ps)
Week 7.
94.1a,b, 94.2a,b from
94. Taylor's formula
(postscript).
/stig