MA 2108, Fall 2003

Advanced Calculus II



Lecturer: J. Wu
Tutors: J. Wu, Y. Yang Lu Xiliang. (e-mail: g0202184@nus.edu.sg).
Graders: Yang Jialiang (e-mail:g0306107@nus.edu.sg), Zheng Zheng (e-mail:g0301175@nus.edu.sg).
Office: S14, 04-07, Faculty of Science, Lower Kent Ridge Road.
Office Hours: Tuesday 2-5 pm
e-mail: matwuj@nus.edu.sg
Phone: 6874-4940.
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 (consisting of 89 pages).
  • If you dislike the above packed lecture notes, you can download this unpacked lecture notes (consisting of 251 pages).
  • Syllabus
    Sequences of real numbers, series of real numbers, sequences and series of functions.
  • Triangular Numbers
  • Hexagonal numbers
  • Convergence of a sequence
  • Lectures: Tuesday 12-2 pm LT23; Friday 12-2 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 9-10, S4A-03-01
  • Group 2: Wednesday 10-11, S4A-03-01
  • Group 3: Wednesday 11-12, S4A-03-01/02
  • Group 4: Wednesday 12-1, S4A-03-01
  • Group 5: Thursday 12-1, S9A-01-02
  • Group 6: Thursday 1-2, S9A-01-02
  • Group 7: Thursday 2-3, S9A-01-02
  • Group 8: Thursday 3-4, S9A-01-02
  • Group 9: Friday 2-3, S13-05-01
  • Group 10 (long Tutorial):Friday 4-6, S13-05-07
  • 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, 12-1:30 pm, LT23, covering chapters 1 and 2.
  • Final Exam: 22/11/2003 (Sat) 9 am (From the Examination Time-Table of NUS.)
  • 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.
  • Your marks from take-home exams and the midterm exam
  • Instruction:
    1. 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.
    2. If you are not sure about the matriculation or you could not find yourself in the file, please send an e-mail to me for confirmation.
  • 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 29
    Hand in your papers to: the Mailbox on the 1st floor of S14.
    The answers.
  • Take-home Exam 2
    deadline: Friday, September 12
    Hand in your papers to: the Mailbox on the 1st floor of S14.
    The answers.
  • Take-home Exam 3
    deadline: Friday, September 27.
    Hand in your papers to: the Mailbox on the 1st floor of S14.
    The answers.
  • Take-home Exam 4
    deadline: Friday, October 11.
    Hand in your papers to: the Mailbox on the 1st floor of S14.
    The answers.
  • Take-home Exam 5
    deadline: Friday, October 24.
    Hand in your papers to: the Mailbox on the 1st floor of S14
    The answers.
  • Take-home 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
  • Solutions to the midterm exam
  • 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 ֮(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