Instructor: Prof. J. H. Shapiro

Office: D304 Wells Hall,Phone: 3-3831

Office Hours: MWF 11:30--12:20, and by appointment.

email: shapiro@math.msu.edu

Text: D. Sarason, Notes on Complex Function Theory (required).

Prerequisites: You need a good working knowledge of undergraduate-level real analysis, in particular limits and continuity. You must know how to do ``delta-epsilon'' proofs, and be comfortable with notions like ``supremum'', ``limsup, ``infimum'', ``liminf''. You need to be on good terms with the topology of Euclidean space R^n (at least for n=2), especially the concepts of ``open set'', ``closed set'', ``boundary'', and ``compact set''. You must know the fundamental properties of continuous functions (e.g., " a real-valued function that is continuous on a compact set is bounded, and attains its maximum and minimum"), and know how they are proved. You should also have solid experience with multivariable calculus, especially partial derivates and gradients, line integrals, and Green's Theorem.

 

Course Objectives: The course will cover just about all of the text, and additional topics if time permits. The goal is to introduce the student to analytic functions of one complex variable: their fundamental properties, representations, and applications.

Grades: Your preliminary grade for the course will depend solely on examinations and homework: 600 total points, apportioned as follows.

• Midterm Exam: Fri. Feb. 23 (100 pts)
• Final Exam: Mon, April 30 10AM--Noon (200 pts),
• Homework: (300 pts)  Collected periodically (see below).

No exams or homework sets will be dropped. In most cases your preliminary grade will be your final grade. However, other factors, such as: exceptional effort, positive contributions to the classroom experience, improvement over time ... , can play a role in raising your preliminary grade, whereas negative factors such as lack of effort, declining performance, or disruptive behavior can lower it.

 

Homework: Homework problems will be collected roughly once a week. A subset of the problems collected will be graded. In order to get credit for a problem set, you must be present for the entire class at which it is due.

You must write up problems neatly  and logically, providing appropriate explanations of what you are doing. If the grader cannot easily follow your work, you will lose points.

 

Work on the homework problems must be your own! You may discuss with me, or with your classmates any of difficulties you are having with the homework problems, however you must acknowledge any help you get from classmates. If there is persuasive evidence of widespread unacknowledged collaboration, I reserve the right to count exams more and homework less. Cases of flagrant cheating on either homework or exams will be handled according to the University's policy on Integrity of Scholarship and Grades (see Academic Programs 2000-02, page 64). Alternatively, see the Spartan Life website at:
www.vps.msu.edu/SpLife/reg3.htm

and

www.vps.msu.edu/Splife/rule32.htm.

 

 

Policy on Makeup Work: The only valid reasons for missing an exam or a homework assignment are: (1) illness, or (2) a conflicting University activity that cannot be rescheduled. Claims involving such contingencies must be supported by verifiable documentation signed by: (1) your physician in case of illness, or (2) your faculty supervisor in case of a non-rescheduleable University activity. Each case will be handled on an individual basis.

 

Grades of I and DF: Everyone, graduate students and undergraduates, will be graded on the same scale (passing=1.0). Graduate students will be eligible for grades of DF on the same basis that undergraduates are eligible for grades of I (see Academic programs 1995-97, page 50).

 

Specifically: To qualify for a DF or an I, a student must: (a) have completed 12 weeks of the term, but be unable to complete the class because of illness or other compelling reason, and (b) have done satisfactory work in the course, and  in the instructor's judgment, be able to complete the course without repeating it.

 

 

Important Dates:

• Friday, Jan. 12: Close of electronic enrollment
• Monday, January 15: Martin Luther King day---no classes.
• Friday, Feb. 2: Last day to drop a course with 100% refund.
• Wednesday, Feb. 28: Middle of term--last day to drop with no grade.
• Friday, April 27: Last day of class.
• Monday, April 30: Final Exam, 7:45--9:45AM, in the classroom.