Text:  Stephen D. Fisher, Complex Variables, second edition
ISBN-13: 978-0-486-40679-4
 

Office Hours: MW 3:05-4:35, in Room 240, Hill Center, Busch campus. Other good times to talk are right before or right after the class. It is also possible to ask questions by email, which will be generally answered within 24 hours, often sooner. The more detailed your email question is, the more detailed the reply message will be. My email is borisov at rci dot rutgers dot edu.
 

Final Examination: There will be a three-hour final examination given at the end of the semester, May 9, 4pm-7pm, in ARC 205. You must take the final examination at the time scheduled by the university; no final exams will be given earlier. In particular, examinations will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately. If you can not take the final exam due to an emergency, you should let me know as soon as possible.
 

Other examinations and homework: In addition to the final exam, there will be two in-class midterm exams on February 19 and on April 2. Homework will be assigned, but not collected or graded. There will be a one-problem 10 minute quiz on most Wednesdays which will be based on the homework problems.
 

Missed exam/quiz policy: There are no makeups for missed midterm exams or quizzes, regardless of the reason for absence. However, if you can not attend the midterm due to a valid reason, for example a medical emergency, the rest of your scores will be scaled to compensate for the missed test. The same policy applies to the recitation section quizzes. If you have missed or are about to miss a midterm, you should contact me by phone or email as soon as possible. Similarly, you should contact your recitation instructor regarding quiz absences as soon as possible.
 

Miscellaneous: Calculators and notes will NOT be allowed during the midterms and the final. Calculators/notes policy for the quizzes is at the discretion of the recitation instructor.
 

Grading: The course grades will be computed as follows. Each midterm will be graded on a scale from 0 to 100, and the final will be graded on a scale from 0 to 200. You will also receive a recitation score in the range from 0 to 100. At the end of the semester, all these scores are added to give your total score, in the range from 0 to 500. The grades are given according to the total scores, with the distribution of grades likely to mimic historical distribution of grades for this course. Improvement towards the end of the semester is not reflected in the semester grade. Two people with the same total scores will receive the same grade, regardless of who did better at the end of the semester.
 

 

Please try to read the relevant textbook sections before the lecture. Be warned that my lectures may differ from the book in emphasis and structure. You are responsible for both lecture and book material unless otherwise stated in class. However, lecture material is deemed more important.
 

January 22 Section 1.1. Complex numbers and the complex plane
Homework p.9: 1, 3, 5, 9, 11, 13, 19

January 27 Section 1.2. Some geometry
Homework p.20: 1, 3, 7, 9, 11, 21, 23, 29

January 29 Section 1.3. Subsets of the plane
Homework p.28: 1, 3, 5, 7, 9, 13, 25

February 3 Section 1.4. Functions and limits
Homework p.41: 1, 3, 5, 15, 31, 35, 39

February 5 Section 2.1. Analytic and harmonic functions; the Cauchy-Riemann equations
Homework p.84: 2, 5, 9, 15, 23

February 10 Section 2.2. Power series
Homework p.103: 1, 3, 5, 9, 15, 29

February 12 Section 1.5. The exponential, logarithm and trigonometric functions
Homework p.53: 1, 3, 7, 9, 13, 15; p.103: 7, 13, 17, 19

February 17 Review and catch up.

February 19 ***FIRST MIDTERM EXAM***

February 24 Section 1.6. Line integrals and Green's theorem
Homework p.73: 1, 3, 5, 7, 9, 13, 16

February 26 Section 2.3. Cauchy's theorem and Cauchy's formula
Homework p.116: 1, 3, 5, 7, 13, 14, 15

March 3 Section 2.4. Consequences of Cauchy's formula
Homework p.133: 1, 3, 5, 7, 11, 15, 17

March 5 Section 2.4-continued.
Homework p.133: 18, 19, 20, 21, 23

March 10 Section 2.5. Isolated singularities
Homework p.150: 1, 3, 7, 13, 15

March 12 Section 2.5-continued: Laurent series
Homework p.150: 17, 19, 21, 23, 25

March 24 Section 2.6. The residue theorem.
Homework p.167: 1, 3, 5, 7, 8

March 26 Section 2.6-continued: applications
Homework p.167: 9, 11, 15, 17, 27, 29

March 31 Review and catch up.

April 2 ***SECOND MIDTERM EXAM***

April 7 Section 3.1. The zeros of an analytic function
Homework p.179: 3, 5, 9, 11, 17, 23

April 9 Section 3.2. Maximum modulus and mean value
Homework p.194: 1, 3, 5, 9, 15, 17

April 14 Section 3.3. Linear fractional transformations
Homework p.204: 3, 5, 7, 11, 16, 17

April 16 Section 3.4. Conformal mapping
Homework p.218: 1, 2, 3, 5, 15

April 21 Section 3.5. The Riemann Mapping Theorem and Schwarz-Christoffel Transformations
Homework p.241: 1, 3, 5, 13, 15

April 23 Section 4.1. Harmonic functions
Homework p.252: 1, 2, 3, 4, 5, 9

April 28 Section (not in the book). Gamma function
Homework Click to get the notes

April 30 Section (not in the book). Riemann zeta function
Homework Click to get the notes

May 5 Review and catch up.

May 9, 4pm-7pm, ARC 205 ***FINAL EXAM***