Math 4001 Analysis II

Semester 2, 2009-2010

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 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.

Prerequisite:
 Math 3001 Analysis 1 and Math 3130 Linear Algebra.

Course Text:
 We will use the text "Undergraduate Analysis", by Serge Lang, Second Edition, Springer, 2005.

Assessment: Lecture Hours and Venue:
MWF, 11 - 11:50 a.m., ECCR 137.

Consultation Hours:
MWF 3-4 p.m., and by appointment.

Homework Assignments:



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 January 5, 2010.