V63.0325-001: Analysis I
| Term: | Spring 2011 |
| Meeting times: | MW 11:00 a.m. - 12:15 p.m. in WWH 102 Recitation (V63.0325-002): 8:00 - 9:15 a.m. T in Room TBD |
| Instructor: | Prof. Charles Newman |
| Office: | 817 WWH |
| Office hours: | TBD and by appointment |
| Phone: | 212-998-3309 |
| Email: | newman@cims.nyu.edu |
Prerequisites
Prerequisite: V63.0123 Calculus III and V63.0140 Linear Algebra or the equivalent.Goals and Topics
- The main purpose of this class is to study rigorously functions of one real variable, starting from the construction of real numbers
- Topics to be covered: The real number system. Convergence of sequences and series. Rigorous study of functions of one real variable: continuity, connectedness, compactness, metric spaces, power series, uniform convergence and continuity.
Course Details
Textbook and Materials
An Introduction to Analysis by William R. Wade, 4th
Edition, Pearson Prentice Hall. For extra reading (but not
required): Real Mathematical
Analysis by Charles C. Pugh, Springer.
Homework
Homework will be assigned weekly, and collected during recitations (and handed back also during recitations, the week after. ) For fairness reasons, late homework will not be accepted, but the lowest homework grade will be dropped to compute the final grade.Exams
Midterm Exam: The midterm exam will be during a regular class
period; the exact date is to be determined.
Final Exam: The final exam is currently scheduled on Monday,
May 16th, 10 a.m. - 11:50 a.m.
[NOTE: THIS BEGINS ONE HOUR BEFORE THE USUAL CLASS TIME] and the
room will be determined later [MAY NOT BE IN THE USUAL ROOM].
Note that we will not be able to accommodate early finals for
non-academic, non-emergency reasons: please plan your travel
schedule accordingly.
NB: The first class in on Monday, January 24 and the last class is
on Monday, May 9. There will be no class on Monday, February 21
(Presidents Day) or during Spring Break (March 14 - 19).
Grading policy
Homework, Midterm Exam and Final Exam will all count. A more
precise grading policy is to be determined.
Tentative Calendar
| Week | Topic |
|---|---|
| 1, 2, 3 |
the set of real numbers: construction properties |
| 4, 5, 6 |
convergence of sequences, compactness |
| 7, 8, 9 |
functions of one real variable: continuity, differentiation,
Riemann integration (the simplest notion of integration |
| 10, 11, 12 |
series: convergence, properties |
| 13, 14, 15 |
convergence of functions: pointwise and uniform
convergence |