MA 2108, Fall 2002

Advanced Calculus II



Lecturer: J. Wu
Tutors: S. K. Chua, J. Wu
Office: S14, 04-07, Faculty of Science, Lower Kent Ridge Road.
Office Hours: Friday 2-5 pm
e-mail: matwuj@nus.edu.sg
Phone: 874-4940.
Text Books:
  1. Manfred Stoll, Introduction to real analysis, 2nd Edition, Addison Wesley Longman, Inc. press, 2001.
  2. 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.
  • Syllabus
    Sequences of real numbers, series of real numbers, sequences and series of functions.
  • Lectures: Tues 2-4 pm LT23; Thu 12-2 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 4-6 pm, S14 03-10 (CRA)
  • Group 1: Wednesday 9-10 am, S4A 03-02
  • Group 2: Wednesday 10-11 am, S4A 03-02
  • Group 3: Wednesday 11-12, S4A 03-02
  • Group 4: Wednesday 12-1 pm, S4A 03-02
  • Group 5: Friday 12-1 pm, S4A 03-02
  • Group 6: Friday 1-2 pm, S4A 03-02
  • 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, 2-3:30 pm, LT 23, covering chapters 1 and 2.
  • Final Exam: 20/11/2002 (Wed) 12:30
  • 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%.
  • Rules for the Exams:
    1. NO Make-up exams.
    2. During the final exam, a help sheet (two-sided up to A4 size) is allowable.
    3. 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.
  • Take-home Exam 1
    deadline: Friday, August 23
    Hand-in your papers to: the general office of the Math Department, the 3rd floor of S14
    The answers.
  • Take-home 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.
  • Take-home 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.
  • Take-home 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.
  • Take-home 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.
  • Take-home 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 ֮(430-501)
    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