Home Page of MA 2108 and MA2108S

		MA 2108, Fall 2005 Advanced Calculus II

Lecturer: J. Wu (e-mail:

 
matwuj@nus.edu.sg

)

Tutors: J. Wu (e-mail:

 
matwuj@nus.edu.sg

) and Jelena Grbic (e-mail: matgj@nus.edu.sg).

Graders: Yang Jialiang (e-mail: g0306107@nus.edu.sg), Chen Yidi (e-mail: yidi@nus.edu.sg) .

Office: S14, 04-07, Faculty of Science, Lower Kent Ridge Road.

Office Hours: Friday 2-4pm or by making appointment through e-mail

e-mail:

 
matwuj@nus.edu.sg

Phone: 6874-4940.

Problem-based learning of this module

Announcement

Important Notes on MA2108 and MA3110

Text Books:

R. G. Bartle and D. R. Sherbert, Introduction to real analysis, 3rd edition, John Wiley, 2000. (Compulsory reading)
Relevant Sections and Suggested Exercises from Bartle and Sherbert's book
W. Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, 1976. (Supplementary reading)
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 235 pages.

Packed lecture notes 85 pages

Syllabus

Completeness axiom of the real number system. Sequences, limits (epsilon-N definition), monotone convergence theorem, Cauchy's criterion for convergence, sup, inf, lim sup and lim inf of a sequence. Infinite series, Cauchy's criteria, absolute and conditional convergence. Tests for convergence. Power series and the radius of convergence. Review of the elementary functions and their properties via power series. Pointwise and uniform convergence of a sequence of functions, Weierstrass M-test. Integration and differentiation of a series of functions.

Triangular Numbers

Hexagonal numbers

Convergence of a sequence

Lectures: Tuesday 10-12 LT25; Friday 10-12 LT 25.

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 (ST1): . Group 2 (ST2): . Group 3 (ST3): . Group 4 (ST4,STL): . Group 5 (ST5): . Group 6 (ST6): . Group 7 (ST7):. Group 8 (ST8): .

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, 11 October, LT25, covering chapters 1 and 2.

Final Exam: 29/11/2005 (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:

NO Make-up exams.
The final exam is a closed book exam, but you are allowed to bring along TWO help sheets.
The midterm exam is a closed book exam, but you are allowed to bring along One help sheet.
Definition of a help sheet: A help sheet is a piece of paper of size not larger than A4 (21 cm by 30 cm). Anything on the help sheet must be handwritten and may be written on both sides of the paper. The handwriting can be as big or as small as the candidate may desire. However, the help sheet must not contain any machine printed information of any kind (such as photocopy of a page from either a book or handwritten notes.)