Math 4310 Introduction to Analysis Fall '07
Semester 1, 2007-08
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 Information:
This course is meant to familiarize the student with the theory of
functions of one real variable.
Topics to be covered include:
the real number system; limits of sequences of real numbers,
functions of one real variable,
continuity, differentiation, the Riemann integral, sequences and series of functions,
convergence and uniform convergence, and Taylor's Theorem.
Prerequisite:
Math 2400 Calculus 3 and Math 3000 or Math 3200. Math 3130 Linear Algebra is highly recommended.
Course Text:
We will use the text "Elementary Analysis: The Theory of the Calculus", by Kenneth A. Ross, Springer.
Assessment:
- Assessment of homework performance: 20 % of final grade
- In-class mid-term exam - Monday, October 1, 10 - 11 a.m. : 25 % of final grade.
- Click HERE for a review sheet for the exam.
- Click HERE for solutions to the exam.
- In-class mid-term exam - Monday, November 5, 10 - 11 a.m. : 25 % of final grade.
- Click HERE for a review sheet
for the exam.
- Click HERE for solutions to the
exam.
- Click HERE for a partial review sheet for the final exam. Also refer to the two midterm review sheets.
- Click HERE for some
solutions to the above partial review sheet.
- Final exam - in class, Tuesday, December 18, 7:30 a.m. - 10 a.m. : 30 % of final grade.
Lecture Hours and Venue:
MWF, 10 - 10:50 a.m., ECCR 110 (NOTE ROOM CHANGE!)
Consultation Hours:
MW 3-4, F 11-12 and by appt.
Homework Assignments:
- Assignment 1: p.5, 1.1, 1.2; p. 12, 2.2, 2.6; p. 18-19, 3.1 (a), (b), 3.5 (a), (b), 3.7 (a), (b), (c), 3.8;
due Wed. Sept. 5.
- Click HERE for some solutions to Assignment 1.
- Assignment 2, due Mon. Sept 10: 4.1 (e), (n), (u),(t), 4.2 (e), (k), (v), 4.3 (k),(m), 4.6(a), 4.7(a), (b), 4.8(b).
- Click HERE for some solutions to Assignment 2.
- Assignment 3, due Mon., Sept. 17: p. 26, 4.10, 4.12, 4.15; p. 36: 7.1 (a), (d), 7.2 (a). (d), 7.3 (c) (i), (j), (m), (o), (p); 7.4 (a), (b); p. 42; 8.1 (a)(c).
- Click HERE for some solutions to Assignment 3.
- Assignment 4, due Mon., Sept. 24: 8.2(a),(b), 8.3, 8.4, 8.5(a). 8.8(b), 9.2(a),(b), 9.4(a), (b). 9.10(a).
- Click HERE for some solutions to Assignment 4.
- Assignment 5, due Monday, October 8: Read Sections 10 and 11, and do problems p. 62: 10.1 (a) (d) (f), 10. 6(a), p. 73 11.1(a), 11.2 (d), (e), 11.5(a), (b).
- Click HERE for some solutions to
Assignment 5.
- Assignment 6, due Monday, October 15: Read Sections 12, 14 and 17 through p. 118; do problems p. 78 12.2, 12.6(a), 12.10; pp. 98-99 14.1 (a), (c), (d), (e), 14.6 (a); p. 123 17.2 (a), (b).
- Click HERE for some solutions to
Assignment 6.
- Assignment 7, due Monday, October 22: Finish reading Section 17 and read
Section 18; do problems p. 123-124 17.3 (e),(f), 17.8 (a), 17.10 (b), (c), 17.12(a); p. 131-132 18.1, 18.5 (a), 18.10.
- Click HERE for some solutions to
Assignment 7.
- Assignment 8, due Monday, October 29: Read Section 19; do problems
pp. 144-145 19.1 (a), (b) (e), 19.2 (a), 19.4 (a), 19.5 (b), 19.9.
- Click HERE for some solutions to
Assignment 8.
- Assignment 9, due Wednesday, November 14: Read Section 20 and Section 24;
do problems p. 155 20.3, 20.11, 20.16, 20.18; p. 182 24.2 (a), (b).
- Click HERE for some solutions to
Assignment 9.
- Assignment 10, due Wednesday, November 28: Read Sections 23, 25, and the
first half of Section 28. do problems p. 176-177 23.1 (d),(f),(g), 23.2 (d), 23.5(a); p. 183-184, 24.4,24.6(a),(b), 24.17, p. 191 25.6 (a),(b), p. 211-212 28.4(b).
- Click HERE for some solutions to
Assignment 10.
- Assignment 11, due Wednesday, December 5: Read second half of Section 28, Section 29, Section 26, and Section 31; do problems p. 212, 28.6 (b), 28.8 (b), (c); p. 221 29.11, 29.12(b),(c); p. 199 26.3 (a), (b), p. 240 31.1.
- Click HERE for some solutions to
Assignment 11.
- Assignment 12, due Friday, December 14: Read Section 32, 33, 34; do problems pp. 252-253 32.3, 32.6, pp. 260-261 33.4, p. 190 25.3 (a), (b); pp. 199-200 26.4(b).
- Click HERE for some solutions to
Assignment 12.
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.
Students With Disabilities:
If you qualify for accommodations because of a disability, please submit a
letter to me from Disability Services in a timely manner so that your needs may
be addressed. Disability Services determines accommodations based on
documented disabilities. Contact: 303-492-8671, Willard 322, or
www.Colorado.EDU/disabilityservices
Disability Services' letters for students with disabilities indicate
legally-mandated, reasonable accommodations.
The syllabus statements and answers to Frequently Asked Questions can be found
at
www.colorado.edu/disabilityservices/accommodations.html
Missed Exams:
If you are absent from an exam without a valid excuse, you will receive a
grade of "F" for that exam. Examples of valid excuses are: documented illness
(doctor's letter required), religious observance, serious family emergency.
Leaving early for or coming back late from an out-of-town trip is not considered
a valid excuse for being absent from an exam.
Religious Obligations:
Campus policy regarding religious observances requires that faculty make every
effort to reasonably and fairly deal with all students who, because of
religious obligations, have conflicts with scheduled exams, assignments or
required attendance. In this class,
if you have a religious obligation that conflicts with one of the exams,
please let your instructor know at least two weeks in advance.
See policy details at
http://www.colorado.edu/policies/fac_relig.html
Student Classroom and Course-Related Behavior:
Students and faculty each have responsibility for maintaining an
appropriate
learning environment. Students who fail to adhere to such behavioral standards
may be subject to discipline. Faculty have the professional responsibility to
treat all students with understanding, dignity and respect, to guide classroom
discussion and to set reasonable limits on the manner in which they and their
students express opinions. Professional courtesy and sensitivity are
especially important with respect to individuals and topics dealing with
differences of race, culture, religion, politics, sexual orientation, gender,
gender variance, and nationalities. Class rosters are provided to the
instructor with
the student's legal name. I will gladly honor your request to address you by an
alternate name or gender pronoun. Please advise me of this preference early in
the semester so that I may make appropriate changes to my records.
See policies at
http://www.colorado.edu/policies/classbehavior.html
and at
http://www.colorado.edu/studentaffairs/judicialaffairs/code.html#student_code
Honor Code:
All students of the University of Colorado at Boulder are responsible for
knowing and adhering to the academic integrity policy of this institution.
Violations of this policy may include: cheating, plagiarism, aid of academic
dishonesty, fabrication, lying, bribery, and threatening behavior. All
incidents of academic misconduct shall be reported to the Honor Code Council
(honor@colorado.edu; 303-725-2273). Students who are found to be in violation
of the academic integrity policy will be subject to both academic sanctions
from the faculty member and non-academic sanctions (including but not limited
to university probation, suspension, or expulsion). Additional information on
the Honor Code can be found at
http://www.colorado.edu/policies/honor.html and at
http://www.colorado.edu/academics/honorcode/
Discrimination and Sexual Harassment:
The University of Colorado at Boulder policy on Discrimination and
Harassment, the University of
Colorado policy on Sexual Harassment and the University of Colorado policy on
Amorous Relationships applies to all students, staff and faculty. Any student,
staff or faculty member who believes s/he has been the subject of
discrimination or harassment based upon race, color, national origin, sex, age,
disability, religion, sexual orientation, or veteran status should contact the
Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of
Judicial Affairs at 303-492-5550. Information about the ODH and the campus
resources available to assist individuals regarding discrimination or
harassment can be obtained at
http://www.colorado.edu/odh.
Some famous mathematicians who worked in this area:
Back to the home page of Judith A. Packer
Last modified August 21, 2007.