Completeness axiom of the real number system.
Sequences, limits (epsilon-N definition), monotone convergence theorem,
Cauchy's criterion for convergence, sup, inf, lim sup and lim inf of a sequence.
Infinite series, Cauchy's criteria, absolute and conditional convergence.
Tests for convergence. Power series and the radius of convergence.
Review of the elementary functions and their properties via power series.
Pointwise and uniform convergence of a sequence of functions, Weierstrass M-test.
Integration and differentiation of a series of functions.
Additonal topics of MA2108S:
Conditions equivalent to the completeness axiom, rearrangement of series,
trigonometric series.
Everybody must attend all lectures and should arrive on
time. In case you missed the class due to sick, then you should submit
your MC to me. If you missed some classes without sufficient reasons, you
might get negative credit to your grade from the course.
Group 11 (long Tutorial, STL): FRIDAY 1600-1800 S13-0506.
Tutorial of MA 2108S: S9A-01-02
Wed 2-4 pm.
Everybody must attend tutorials and should arrive on
time. In case you missed any tutorial due to sick, then you
should submit
your MC to me. If you missed some tutorials without sufficient
reasons, you might get negative credit to your grade from the course.
CA, which includes the midterm test, take-home exams, participation
in tutorials and classes, and etc, will be counted as 30% and the
final will be counted as 70%.
Assessment for MA 2108S: CA 50%, which includes tutorial presentation and tests,
and the final 50%.
Rules for the Exams:
NO Make-up exams.
During the final exam, a help sheet (two-sided up to A4 size) is
allowable.
During the midterm exam, a help sheet (two-sided up to
HALF A4 size) is allowable.
Take-home Exams
It is strictly NOT allowed to copy other people's solutions;
but you are allowed to discuss the problems with your classmates.
A
little history about the number Pi:1500 years
ago our ancestor already knew that Pi is between 3.1415926 and
3.1415927. This is really remarkable during the time when nobody knew
any calculus. By using Taylor series together with computer, we obtain
that Pi is about 3.14159264, a little more accurate than what our 1500
years old ancestor
did.
These pictures are created by
Maple. Here
are my Maple commands for the left picture: 1. with(plots,animate); 2.
animate([e/(1+e*sin(125*t)),t,t=0..2*Pi],e=-2..2,coords=polar,view=[-4..4,-4..4],numpoints=150,frames=30);
Have a fun with Math!
