 
MA 2108, Spring 2003
Advanced Calculus II
 

Lecturer: J. Wu
Tutors: X.
W. Xu, J. Wu
Office: S14,
0407, Faculty of Science, Lower Kent
Ridge Road.
Office Hours: Tuesday 46 pm.
email:
matwuj@nus.edu.sg
Phone: 68744940.
Be careful for SARS, but NOT to
be panic. Here
is a presentation for SARS.The updated presentation.
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 85 pages).
If you dislike the above packed lecture notes, you can download this unpacked lecture notes (consisting of 221
pages).
SyllabusSequences of real numbers, series of real numbers,
sequences and series of functions.
Lectures: Tues 24 pm LT22; Fri 24 pm LT 22.
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: Friday 46 pm, S13 0502
Group 1: Tuesday 910 am, S14 0310
Group 2: Tuesday 1011 am, S14 0310
Group 3: Wednesday 910 am, S13 0502
Group 4: Wednesday 1011 am, S13 0502
Group 5: Wednesday 12 pm, S13 0501
Group 6: Wednesday 23 pm, S13 0501 


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: 18/03/2003 (Tuesday) 23:30 pm covering chapters 1
and 2.
Final Exam: 29/04/2003 (Tue) 4:30 PM (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:
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Group 7
Group 8
Instruction:
 The above 8 groups are given according to
your
online registration for tutorial. For instance, if you registered
Tutorial Group 2 (although you may change to other tutorial groups later),
you still check your marks from Group 2 above. If you did not do online
registration, you can check Group 8.
 Your name does not appear in the above files.
 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.
 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: Tuesday, Feburay 4.
Handin your papers to:
the general office of the Math Department, the
3rd floor of S14.
The answers.
Takehome Exam 2
deadline: Friday, Feburary 14.
Hand in your papers to:
the general office of the Math
Department, the 3rd floor of S14.
The answers.
Takehome Exam 3
deadline: Monday, March 3.
Hand in your papers to:
the Mailbox on
the 1st floor of S14.
The answers.
Takehome Exam 4
deadline: Friday, March 14.
Hand in your papers to:
the Mailbox on
the 1st floor of S14.
The answers.
Takehome Exam 5
deadline: Friday, March 28.
Hand in your papers to:
the Mailbox on the 1st floor of S14
The answers.
Takehome Exam 6
deadline: Friday, April 11.
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
Solutions to the final exam
Solutions to the Midterm Exam
Past Midterms
Fall 2002 and
the solutions
Spring 2002 and
the
solutions
Fall 2001 and
the solutions
Summer 2000 with
suggested answers.
Past Finals
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