Matematik och Datavetenskap, Chalmers Tekniska Högskola och Göteborgs Universitet
Each student must keep an individual folder (pärm) containing documentation of the basic, obligatory work. The folder need not be handed in.
Each student must also keep a copy of each obligatory program that we write. These programs may be used in future courses.
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.
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. Show this to one of your teachers during week 2 or 3.
Write down several examples including:
1. an initial-value problem.
2. a solution formula.
3. a Matlab computation with my_int, a plot of the computed solution and the solution formula.
4. hand computation of some steps of the program.
Week 3. My ode solver 1.
Week 4. 92. Analytical computation of integrals (postscript).
Week 5. 93. Analytical solution of differential equations (postscript).
Week 6. 94. Taylor's formula (postscript).
Week 7. None this week.