 
MA 2108, Fall 2003
Advanced Calculus II
 

Lecturer: J. Wu
Tutors: J. Wu,
Y. Yang Lu Xiliang.
(email: g0202184@nus.edu.sg
).
Graders:
Yang Jialiang (email:g0306107@nus.edu.sg
),
Zheng Zheng (email:g0301175@nus.edu.sg
).
Office: S14,
0407, Faculty of Science, Lower Kent
Ridge Road.
Office Hours: Tuesday 25 pm
email:
matwuj@nus.edu.sg
Phone: 68744940.
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 (consisting of 89 pages).
If you dislike the above packed lecture notes, you can download this unpacked lecture notes (consisting of 251
pages).
SyllabusSequences of real numbers, series of real numbers,
sequences and series of functions.
Triangular Numbers
Hexagonal numbers
Convergence of a sequence
Lectures: Tuesday 122 pm LT23; Friday 122 pm LT 23.
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 through CORS)
Group 1: Wednesday 910, S4A0301
Group 2: Wednesday 1011, S4A0301
Group 3: Wednesday 1112, S4A0301/02
Group 4: Wednesday 121, S4A0301
Group 5: Thursday 121, S9A0102
Group 6: Thursday 12, S9A0102
Group 7: Thursday 23, S9A0102
Group 8: Thursday 34, S9A0102
Group 9: Friday 23, S130501
Group 10 (long Tutorial):Friday 46, S130507 


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: Friday, 10 October, 121:30 pm, LT23, covering chapters 1
and 2.
Final Exam: 22/11/2003 (Sat) 9 am (From the
Examination TimeTable of NUS.)
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.
Your marks from takehome exams and the midterm exam
Instruction:
 In the above files, matriculation only takes 4 digital numbers
from your actual matriculation number. For instance, if your matriculation
number is U012345X02, then the matriculation in the file is "2345", in
other words the head "U01" and the tail "X02" are deleted. In case your matriculation number is U020123X02,
then the matriculation in the file is "*0123" for avoiding to start with 0.
 If you are not sure about the matriculation or you could not find
yourself in the file, please send an email to me for confirmation.
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 29
Hand in your papers to:
the Mailbox on
the 1st floor of S14.
The answers.
Takehome Exam 2
deadline: Friday, September 12
Hand in your papers to:
the Mailbox on
the 1st floor of S14.
The answers.
Takehome Exam 3
deadline: Friday, September 27.
Hand in your papers to:
the Mailbox on
the 1st floor of S14.
The answers.
Takehome Exam 4
deadline: Friday, October 11.
Hand in your papers to:
the Mailbox on
the 1st floor of S14.
The answers.
Takehome Exam 5
deadline: Friday, October 24.
Hand in your papers to:
the Mailbox on the 1st floor of S14
The answers.
Takehome Exam 6
deadline: Friday, November 7.
Hand in your papers to:
the Mailbox on
the 1st 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
Past Midterms
Spring
2003 and
the solutions
Fall 2002 and
the solutions
Spring 2002 and
the
solutions
Fall 2001 and
the solutions
Summer 2000 with
suggested answers.
Past Finals
Spring 2003
and
the solutions
Fall 2002
and
the solutions
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