Math 4001-5001 Analysis II
Semester 1, 2016-2017
Course Lecturer:
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
Email: packer@colorado.edu
URL: http://spot.colorado.edu/~packer
Course Syllabus: For course syllabus, complete with list of university policies, click here!
Course Information:
This course is meant to continue to familiarize the student with the theory of
functions of one or more real variables, with an initial emphasis on sequences and series of functions and
different types of convergence, and with a continuation into the theory of vector-valued functions of vector variables,
including the inverse function theorem and the implicit function theorem.
Topics to be covered include:
a rigorous treatment of infinite series of real numbers, sequences and series of functions,
convergence and uniform convergence of sequences and series of functions, Taylor's Theorem,
a brief review of vector spaces, in particular, n-dimensional Euclidean space;
differentiation, including
the definition of the total derivative and the chain rule; the mean value theorem, the inverse mapping theorem,
and the implicit function theorem. This includes most of Chapters 3, 7, 8 and 9 of the textbook.
Prerequisite:
Math 3001 Analysis 1 and Math 3130 Linear Algebra.
Course Text:
We will use the text "Principles of Mathematical Analysis", by Walter Rudin, Third Edition, MacGraw Hill.
Lecture Hours and Venue:
MWF, 3 - 3:50 p.m., ECCR 118.
Consultation Hours:
MWF 1-2 p.m., and by appointment.
Assessment:
- Homework will be assigned every week. Some, but not all, of the problems will be graded. Please note that the assigments
for Math 5001 will include extra problems. The assessment of homework performance will count for 30% of the final grade.
- In-class mid-term exam - Wednesday, September 28, 2016, 3 p.m. - 4 p.m., ECCR 118: 20 % of final grade. You will be allowed a 3" by 5" notecard on this exam.
- Sample first midterm from several years ago.
- Take-home mid-term exam - given out Wednesday, November 2, 2016, 3:50 p.m, due Wednesday November 9, 2016,
3:00 p.m. (please note that takehome exams will be different for Math 4001 and Math 5001): 20 % of final grade.
- Takehome midterm for Math 4001, due November 9, 2016, 3 p.m.
- Solutions to the take-home Midterm for Math 4001.
- Takehome midterm for Math 5001, due November 9, 2016, 3 p.m
- Some solutions to the take-home Midterm for Math 5001.
- In-class final exam - Wednesday, December 14, 2016, 4:30 p.m. - 7 p.m., in ECCR 118 - note the evening hour!
: 30% of final grade.
- Example of past-year final exam for Math 4001/5001.
If you are absent from an exam, or do not hand in the take-home exam on time, without a valid excuse, you will receive a
grade of "F" for that exam. Examples of valid excuse are: documented illness
(doctor's letter required), religious observance, and serious family emergency.
Homework Assignments:
- Assignment 1: Read Chapter 3, pp. 59-68 of the textbook, and do the following problems on pp. 78-80: Math 4001
6 (a),(b),(c),(d), 7,8, 11 (a); Math 5001 do all Math 4001 problems and also do problems 14 (a), (b), (c). Due Wednesday, August 31, 2016.
- Selected solutions to Assignment 1.
- Assignment 2: Continue reading Chapter 3, pp. 69-78 of the textbook, and do the assignment linked here.
Due Friday, September 9, 2016.
- Selected solutions to Assignment 2.
- Assignment 3: begin reading Chapter 7, pp. 143--147 of the textbook. Do the assignment linked here. Students in
Math 5001 should do the assignment linked here, in addition to the previous problems.
Due Friday, September 16, 2016.
- Selected solutions to Assignment 3.
- Assignment 4: Continue reading Chapter 7, pp. 147--153 of the textbook, and do the assignment linked here.
Due Friday, September 23, 2016.
- Selected solutions to Assignment 4.
- Assignment 5: Start reading Chapter 8, pp. 172--178 of the textbook, and do the assignment linked here.
Due Friday, October 7, 2016.
- Selected solutions to Assignment 5.
- Assignment 6: Read Chapter 5, pp. 110-111 of the textbook, and do
the assignment linked here.
Due Friday, October 14, 2016.
- Selected solutions to Assignment 6.
- Assignment 7: Read Chapter 9, pp. 211-218 of the textbook, and do
the assignment linked here.
Due Friday, October 21, 2016.
- Selected solutions to Assignment 7.
- Assignment 8: Read Chapter 9, pp. 218-221 of the textbook, and do
the assignment linked here.
Due Friday, October 28, 2016.
- Selected solutions to Assignment 8.
- Assignment 9: Read Chapter 9, pp. 235-236 of the textbook, and do
the assignment linked here.
Due WEDNESDAY, November 2, 2016.
- Selected solutions to Assignment 9.
- Assignment 10: Read Chapter 9, pp. 221-228 of the textbook, and do
the assignment linked here.
Due Friday, November 18, 2016.
- Selected solutions to Assignment 10.
- Assignment 11: Read Chapter 9, pp. 234-238 of the textbook, and do
the assignment linked here.
Due Friday, December 2, 2016.
- Selected solutions to Assignment 11.
- Assignment 12: Do problems 2, 3, and 6 on the sample old final exam here. If you are in
Math 5001, in addition do problem # 28 p. 242--243. Due Friday, December 9,
2016.
Homework:
Homework will be assigned weekly, and is due at the beginning of class, usually on Mondays.
Some, but not all of the problems will be graded. Show
all your work.
Some famous mathematicians who worked in this area:
Back to the home page of Judith A. Packer
Last modified September 13, 2016.