 
MA 2108, Fall 2002
Advanced Calculus II
 

Lecturer: J. Wu
Tutors: S. K. Chua, J. Wu
Office: S14, 0407, Faculty of Science, Lower Kent
Ridge Road.
Office Hours: Friday 25 pm
email:
matwuj@nus.edu.sg
Phone: 8744940.
Text Books:
 Manfred Stoll, Introduction to
real analysis, 2nd
Edition, Addison Wesley Longman, Inc. press, 2001.
 James Stewart, Calculus, 4th Edition,
Brooks/Cole Publishing Company press, 1999.
Lecture Notes
If you dislike the above packed lecture notes, you can download this unpacked lecture notes consisting of 219
pages.
SyllabusSequences of real numbers, series of real numbers,
sequences and series of functions.
Lectures: Tues 24 pm LT23; Thu 122 pm LT 21.
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.
Tutorials: Online
Registration for Tutorials
Long Tutorial: Tuesday 46 pm, S14 0310 (CRA)
Group 1: Wednesday 910 am, S4A 0302
Group 2: Wednesday 1011 am, S4A 0302
Group 3: Wednesday 1112, S4A 0302
Group 4: Wednesday 121 pm, S4A 0302
Group 5: Friday 121 pm, S4A 0302
Group 6: Friday 12 pm, S4A 0302 


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.
Exams
Midterm: Tuesday, 1 October, 23:30 pm, LT 23, covering chapters 1
and 2.
Final Exam: 20/11/2002 (Wed) 12:30
CA, which includes the midterm test, takehome exams, participation
in tutorials and classes, and etc, will be counted as 30% and the
final will be counted as 70%.
Rules for the Exams:
 NO Makeup exams.
 During the final exam, a help sheet (twosided up to A4 size) is
allowable.
 During the midterm exam, a help sheet (twosided up to
HALF A4 size) is allowable.
Takehome Exams
It is strictly NOT allowed to copy other people's solutions;
but you are allowed to discuss the problems with your classmates.
Takehome Exam 1
deadline: Friday, August 23
Handin your papers to: the general office of the Math
Department, the 3rd floor of S14
The answers.
Takehome Exam 2
deadline: Friday, September 6
Hand in your papers to: the general office of the Math
Department, the 3rd floor of S14
The answers.
Takehome Exam 3
deadline: Friday, September 20
Hand in your papers to: the general office of the Math
Department, the 3rd floor of S14.
The answers.
Takehome Exam 4
deadline: Tuesday, October 8
Hand in your papers to: the general office of the Math
Department, the 3rd floor of S14.
The answers.
Takehome Exam 5
deadline: Tuesday, October 22
Hand in your papers to: the general office of the Math
Department, the 3rd floor of S14.
The answers.
Takehome Exam 6
deadline: Friday, November 1
Hand in your papers to: the general office of the Math
Department, the 3rd floor of S14.
The answers.
Tutorials
Tutorial 1 and the answers
Tutorial 2 and the answers
Tutorial 3 and the answers
Tutorial 4 and the answers
Tutorial 5 and the answers
Tutorial 6 and the answers
Tutorial 7 and the answers
Tutorial 8 and the answers
Tutorial 9 and the answers
Tutorial 10 and the answers
Tutorial 11 and the answers
Practice Problems
Solutions to the Midterm
Exam
Past Midterms
Spring 2002 and
the
solutions
Fall 2001 and
the solutions
Summer 2000 with
suggested answers.
Past Finals
Spring 2002
and
the solutions
Fall 2001 and
the answers
Summer
2000 with
the answers.
Computation of Pi using Taylor series
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.  Tsu Ch'ung
Chi ×æ³åÖ®(430501) 

Links to Calculus at Other Universities
Calculus
II at the University of Pennsylvania.
Calculus at
Harvard

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!



Maple
commands
for the right picture above.
More
pictures.
Feedback on matters related to the course will be welcome. Please send
it to
matwuj@nus.edu.sg