APPM 5440
Applied Analysis
Fall 2014
http://amath.colorado.edu/content/appm-5440-applied-analysis-1-fall-2014
Instructor and contacts: S. Becker, ECOT 231, (303) 492-0663, stephen.becker@colorado.edu. I will respond to most
reasonable email, but (1) lengthy questions should be posed at office hours and not via email, and (2) I will not
check email at odd hours or just before homework is due.
Meeting times: Monday, Wednesday and Friday, ECCR 257, 10:00 AM to 10:50 AM.
Office hours: Wednesdays 2-3 and 4-5 PM, Thursdays 3-4 PM.
Course Content and Goals: Analysis extends calculus to more general settings and is the foundation of applied mathematics. This course, along with the second semester (APPM 5450), provides an introduction to the fundamental
mathematical spaces (Banach, Hilbert, Sobolev), and extends calculus concepts (limits, derivatives, integrals) to
more powerful concepts (convergence and completeness, measure theory). Thought-process and proof technique
are emphasized over memorization of definitions. The course is designed hand-in-hand with the applied analysis
qualifying exam for applied math graduate students.
The course is applied analysis because the topics are selected to be useful for applied mathematicians, and not
because we will discuss applications in depth. For example, in comparison with a graduate class in analysis in the
math department, we will emphasize topics like Fourier analysis and existence of solutions to differential equations,
and not cover topics like non-metric topologies or discuss the axiom of choice.
Text: Applied Analysis by John K. Hunter and Bruno Nachtergaele. Real analysis texts, such as those by Kolmogorov
and Fomin, or Royden, may also be useful, but are optional.
Syllabus: Roughly, chapters 1–6 of the text. In particular, we will cover all of the material in chapters 6 and earlier
that is mentioned at http://amath.colorado.edu/content/applied-analysis-preliminary-exam-syllabus.
Electronic devices policy: Please refrain from using your cell phone in class; if you have to make an important
call/text/email, please leave the classroom temporarily. Laptops and tablets are reasonable if they are used
for note-taking purposes, but please sit in the back of the class to avoid distracting students sitting behind
you. There is some recent research showing a correlation between less device usage and higher grades; see
http://assett.colorado.edu/distracted-by-the-digital-age/
Recitations: There is no recitation session. If you would like additional discussion of the material, please come to office
hours.
Grading: There will be weekly homework and a final exam.
Each homework will have two types of problems:
• Collaboration problems: collaboration with your fellow students is OK and in fact recommended, although direct copying is not allowed. The internet is allowed for basic tasks (e.g., looking up definitions
on wikipedia) but it is not permissible to search for proofs or to post requests for help on forums such as
http://math.stackexchange.com/. On these problems, please write down the names of the students that
you worked with.
• No collaboration problems (mini open-book take-home exams): collaboration with anyone is forbidden.
Internet usage is forbidden.
For both types of homework, you may use the course book or the supplemental books by Kolmogorov and Fomin
or Royden, but no other books.
On each homework, an arbitrary selection of problems will be graded.
The final exam (Tuesday, Dec. 16, 10:30 AM to 1 PM) will be 2.5 hours long, in-class, and closed book. It will be
designed to be similar in style to the applied math preliminary exam in applied analysis. The final exam schedule
is available at http://www.colorado.edu/registrar/calendars-schedules/final-exams-schedule. Students
must take the exam at the schedule time unless (1) they have 3 exams the same day or 2 exams at the same time
[in this case, inform the instructor at least one month prior], or (2) unforeseen emergences such as illness (with a
note from a doctor).
The overall grade will be an equal weight of collaboration-allowed homework, no-collaboration-allowed homework,
and the final. Grades will be available on D2L (http://learn.colorado.edu).
Late homework policy: Homework is due at the beginning of class. Late homework will not be accepted or
graded. Because of this, your lowest scoring homework will be automatically dropped from the final grade calculation (and for this purpose, the collaboration/no-collaboration homeworks will be treated separately).
Course web page: (http://amath.colorado.edu/content/appm-5440-applied-analysis-1-fall-2014 ) It is your
responsibility to check the web page on a regular basis. Here you will find detailed information such as homework
assignments and solutions, office hours, and special announcements. In addition, it contains policies on illness,
academic honesty, and special accommodations for religious holidays and documented special needs.
Dropping the course: Advice from your department advisor is recommended before dropping any course. After Sept
10, dropping a course results in a “W” on your transcript. After Oct 31, dropping the course is possible only with
a petition approved by the Dean’s office.
Academic Honesty and Collaboration policy: For the collaboration-allowed homework, students can, and should,
study with others, however, all work turned in must be your own. Please write down the names of students
that you worked with.
On the no-collaboration homework section, and on the final exam, absolutely now work with others is allowed.
Violation of the CU Student Honor Code (www.colorado.edu/policies/student-honor-code-policy) will result
in an automatic final grade of F in this course.
The following policies are standard CU-Boulder policies:
Disability: If you qualify for accommodations because of a disability, please submit to your professor a letter from
Disability Services in a timely manner (for exam accommodations provide your letter at least one week prior to the exam)
so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities.
Contact Disability Services at 303-492-8671 or by e-mail at dsinfo@colorado.edu. If you have a temporary medical condition
or injury, see Temporary Medical Conditions: Injuries, Surgeries, and Illnesses guidelines under Quick Links at Disability
Services website and discuss your needs with your professor.
Religious holidays: Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and
fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required
attendance. In this class, there should be little conflict since the grade is based on homeworks and a single final exam. If
you must miss the final exam due to religious reasons, talk to the professor at the beginning of the semester to make special
arrangements. If the homework is due on the date of a religious holiday, you are expected to turn the homework in early.
If you have a religious holiday that lasts longer than one week, and so therefore you would not receive the homework with
enough time to turn it in early, talk to the professor at the beginning of the semester. Full details of the campus-wide policy
are at http://www.colorado.edu/policies/fac relig.html.
Classroom behavior: Students and faculty each have responsibility for maintaining an appropriate learning environment. Those
who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, color, culture, religion, creed, politics,
veteran’s status, sexual orientation, gender, gender identity and gender expression, age, disability, and nationalities. Class
rosters are provided to the instructor with the student’s legal name. The instructor will gladly honor your request to address
you by an alternate name or gender pronoun. Please advise your instructor of this preference early in the semester so that we
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.
Harassment and discrimination: The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive
learning, working, and living environment. The University of Colorado does not discriminate on the basis of race, color,
national origin, sex, age, disability, creed, religion, sexual orientation, or veteran status in admission and access to, and
treatment and employment in, its educational programs and activities. (Regent Law, Article 10, amended 11/8/2001). CUBoulder will not tolerate acts of discrimination or harassment based upon Protected Classes or related retaliation against
or by any employee or student. For purposes of this CU-Boulder policy, ”Protected Classes” refers to race, color, national
origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, or veteran status.
Individuals who believe they have been discriminated against should contact the Office of Discrimination and Harassment
(ODH) at 303-492-2127 or the Office of Student Conduct (OSC) at 303-492-5550. Information about the ODH, the above
referenced policies, and the campus resources available to assist individuals regarding discrimination or harassment can be
obtained at http://hr.colorado.edu/dh/.
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; 303-735-2273). 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). Other information on the Honor Code can be found at
http://www.colorado.edu/policies/honor.html and at http://honorcode.colorado.edu.
Note: sanctions for first-time offending graduate students are typically more severe than for first-time offending undergraduate students, since graduate students are held to higher standards.