 
MA 2108, Spring 2002
Advanced Calculus II
 

Lecturer: J. Wu
Tutors: J. Wu
Office: S14, 0407, Faculty of Science, Lower Kent
Ridge Road.
email:
matwuj@nus.edu.sg
Phone: 8744940.
Text Books:
 William R. Parzynski and Philip W. Zipse, Introduction to
mathematical analysis, International Edition 1987, McGrawHill Book
Company Press.
 G. B. Thomas, Jr. and Ross L. Finney, Calculus and analytic
geometry, 9th Edition, International Student Edition, AddisonWesley
Longman Inc. Press, 1996.
 M. Braun, Differential equations and their applications, 3rd
Edition, Applied Mathematical Sciences V. 15, SpringerVerlag, 1986.
Course Outline
Lecture Notes
Supplement to Section 3.9
Supplement to Section 3.10
Lectures: Monday, Thursday, 4:005:30 pm, LT26.
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:
Group 1: Tuesday 1112, S13 0501
Group 2: Tuesday 121, S13 0501
Group 3: Tuesday 12, S13 0501
Group 4: Wednesday 45, S13 0502
Group 5: Friday 45, S13 0506
Group 6: Friday 1012, S13 0404   

Everybody must attend all tutorials and should arrive on
time. In case you missed the tutorial due to sick, then you should
submit your MC to your tutor. If you missed some tutorials without
sufficient reasons, you might get negative credit to your grade from the
course.
Exams
Midterm: (Tentative time) Monday, March 18, 4:005:30, LT26,
Final Exam: Monday, April 22, EV.
CA, which includes the midterm test, participation in tutorials and
classes, and etc, will be counted as 20% and the
final will be counted as 80%.
Rules for the Exams:
 NO Makeup exams.
 During the final exam, a note sheet (twosided up to A4 size) is
allowable.
 During the midterm exam, a note sheet (twosided up to
HALF A4 size) is allowable.
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
Practice problems for Chapter One and
the answers
Practice Exam for the
Midterm and
the solutions
If you like to practice more,
here
is another one with
suggested answers.
For convergence/divergence of series, there are a
lot of questions in one of our text books (ThomasFinney's book "Calculus
and analytic geometry"). So you can find some questions there for
practice.
Solution of the Midterm Exam
Practice exam for the final and the answers
If you like to practice more,
here
is another one with
the answers.
Solution of the Final Exam
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