Instructor: Victor Roytburd (Amos Eaton 405, Ph. 276-6889, roytbv@rpi.edu)
Tentative office hours: Mo, Th, 2-3 (or by appointment)
Teaching Assistant: Ildar Khanov (Amos Eaton 430, (Amos Eaton 430, mailto:khanoi@rpi.edu)
Office hour: Tu 10-11
Class meets: Mo, Th 12:00-1:50, CA
101
We plan a discussion session:
Wednesday 5-7, CA 102
Web-page: www.rpi.edu/~roytbv/ma2/ma2.htm
Textbook:
R. S. Strichartz, The Way of Analysis
Homework: There will be weekly homework assignments that will be collected and graded. As a rule, homework assignments will be due on Monday.
Tests: There will be two tests and a final. The term tests might be partially take home
Grading: Homework 35%, Tests 40%, Final 25%
Statement of academic integrity: The guiding principle is that the work that you present for grading as your own should in fact be your own. With respect to exams, this means that no assistance or collaboration of any kind is permitted. With respect to homework, you are free to seek assistance from any person, or book. You are encouraged to collaborate on homework problems and discuss them with your classmates, but before working together on the homework, you must think over the problems on your own. You must write up your solutions alone. You are not allowed to just copy from a shared (or someone else's) set of notes.
Material covered in Math Analysis I: Strichartz: Chapters 1-6.
This course is a continuation of Math Analysis I. As in that course, the emphasis will be on the conceptual understanding of calculus and on mathematical rigor. To give you some perspective, I list here some important results that we will examine in the course.
- Pointwise and uniform convergence of functional sequences and series.
- Transcendental functions.
- Euclidean and metric spaces.
- Multivariable differential calculus, including the chain rule and Taylor's formula.
- The inverse and implicit function theorems; curves and surfaces.
- Multiple integrals.
Time permitting, we will select additional topics from the following list
- Approximation by polynomials; equicontinuity
- Existence theory for ordinary differential equations
- Fourier series
- The Lebesgue integral
- Line and surface integrals; integral theorems of vector calculus
I don't have any rigid agenda as to how much material to cover. The pace of the course will be mostly determined by our progress, which will be measured by the performance on the homework assignments and tests.
|
WEEK |
CHAPTER |
COMMENTS |
|
Jan 13-31 |
7.2-7.4, 8.1-8.2 |
|
|
Feb 3-7 |
8.2-9.1 |
|
|
Feb 10-14 |
9.1-9.2 |
|
|
Feb 18-21 |
9.2-9.3.3 |
|
|
Feb 24-28 |
Review, Test1 |
Test on material including 9.3.3 |
|
March 3-7 |
9.3.4, 11.1.1-2 |
|
|
March 10-14 |
7.2-9.3.4 |
SPRING BREAK |
|
March 17-21 |
10.1-10.2 |
|
|
March 24-28 |
10.2; 13.1 |
|
|
Mar 31-Apr 4 |
13.1-13.2 |
|
|
Apr 7-11 |
13.3-13.4 |
|
|
Apr 14-18 |
15.1.1, 15.2.1 |
Test 2 on material including 13.4 |
|
Apr 21-25 |
15.2.1-2; 12.1 |
|
|
Apr 28-30 |
12.2.1 |
|
|
May 6 |
11:30-2:30 |
Final Exam Amos Eaton 216 |
SUMMARY
OF COURSE TOPICS
Homework 1, due Jan 23, POSTPONED UNTIL MONDAY JANUARY 27
Homework 2, PS-file due February 3
Problem #5 of homework 3 is concerned with complete spaces
that we didn’t discuss in class. Because of this the due date is extended to
Tuesday February 18 (NO CLASS ON MONDAY).
Correction: In problem #2 in the hint: To get the answer in the book you have
to use both the TRIANGLE AND Cauchy-Schwarz inequalities. (There are
other answers as well, less precise but simpler to get). Homework 3 Selected solutions
Homework 4 , due February 24
SUMMARY OF
THE MATERIAL FOR TEST 1
Homework 5, due March 24
Homework 6, due March 31. For the 3rd problem the number is missing: it should be 15(a).
Homework 7, due April 10 (The comment that the first two problems are to help you
with the notation does not belong here.)
Homework 8, this homework contains
some problems that are representative of those on the final.
REVIEW SESSION: MONDAY, MAY 5, 2-4PM, RM 402 AMOS
EATON