Schedule

Notes

• The schedule is tentative and will change as the course progresses.

• For information about add/drop dates and other matters related to course registration, please consult the Registrar's Website.

• All dates and times are in ET (Eastern Time).

• Section numbers are as in Complex Variables (2nd Edition) by Stephen D. Fisher.

• There will usually be one homework assignment due on Saturday every week.

Week of January 12th (Week 1)

• Classes begin on Tuesday, January 13th.

Tuesday, January 13th

• Topics: the complex numbers, \(\mathbb{C}\), and their construction; the algebra of \(\mathbb{C}\); modulus, conjugate, real part, and imaginary part.

• Reading: §1.1 The Complex Numbers and the Complex Plane.

• Video: (Kaltura01)

Thursday, January 15th

• Topics: the fundamental theorem of algebra; the geometry of \(\mathbb{C}\) via the Argand plane; the geometry of addition, conjugation, and magnitude; polar coordinates and the geometry of multiplication; de Moivre's theorem and its corollaries.

• Reading: §1.1 The Complex Numbers and the Complex Plane; §1.2 Some Geometry.

• Video: (Kaltura02)

• Note: due to a technical issue with the webcam, the Kaltura02 recording only begins halfway through class.

Week of January 19th (Week 2)

• HW 1 is due on Saturday, January 24th at 11 PM.

Tuesday, January 20th

• Reading: §1.3 Subsets of the Plane.

Thursday, January 22nd

• Reading: §1.4 Functions and Limits.

Week of January 26th (Week 3)

• HW 2 is due on Saturday, January 31st at 11 PM.

• I will be out of town for part of this week; please see below for necessary adjustments.

• No Office Hours on Tuesday this week (in view of my travel).

Tuesday, January 27th

• Online Class (via Zoom).

• Reading: §1.3 The Exponential, Logarithm, and Trignometric Functions.

Thursday, January 29th

• Reading: §1.6 Line Integrals and Green’s Theorem.

Week of February 2nd (Week 4)

• HW 3 is due on Saturday, February 6th at 11 PM.

Tuesday, February 3rd

• Reading: §2.1 Analytic and Harmonic Functions; the Cauchy–Riemann Equations.

Thursday, February 5th

• Reading: §2.1 Analytic and Harmonic Functions; the Cauchy–Riemann Equations.

Week of February 9th (Week 5)

• HW 4 is due on Saturday, February 14th at 11 PM.

• I will be out of town for part of this week; please see below for necessary adjustments.

• No Office Hours on Tuesday this week (in view of my travel).

Tuesday, February 10th

• Reading: §2.2 Power Series.

Thursday, February 12th

• Review for Midterm 1.

Week of February 16th (Week 6)

• Midterm 1 is on Monday, February 16th from 8:00 PM to 9:00 PM in LWSN B155.

• HW 5 is due on Saturday, February 21st at 11 PM.

• Extra Office Hours on M, 4:00 PM to 6:00 PM this week (in addition to usual Office Hours) in view of Midterm 1.

Tuesday, February 17th

• Reading: §2.3 Cauchy’s Theorem and Cauchy’s Formula; §2.4 Consequences of Cauchy’s Formula.

Thursday, February 19th

• Reading: §2.3 Cauchy’s Theorem and Cauchy’s Formula; §2.4 Consequences of Cauchy’s Formula.

Week of February 23rd (Week 7)

• HW 6 is due on Saturday, February 27th at 11 PM.

Tuesday, February 24th

• Reading: §2.5 Isolated Singularities.

Thursday, February 25th

• Reading: §2.6 The Residue Theorem and Its Application to the Evaluation of Definite Integrals.

Week of March 2nd (Week 8)

• HW 7 is due on Saturday, March 7th at 11 PM.

Tuesday, March 3rd

• Reading: §2.6 The Residue Theorem and Its Application to the Evaluation of Definite Integrals.

Thursday, March 5th

• Reading: §3.1 The Zeros of an Analytic Function.

Week of March 9th (Week 9)

• HW 8 is due on Saturday, March 13th at 11 PM.

Tuesday, March 10th

• Reading: §3.1 The Zeros of an Analytic Function.

Thursday, March 11th

• Reading: §3.2 Maximum Modulus and Mean Value.

Week of March 16th (Week 10)

• No HW due this week (in view of Spring Break).

Tuesday, March 17th

• No Class (Spring Break).

Thursday, March 18th

• No Class (Spring Break).

Week of March 23rd (Week 11)

• HW 9 is due on Saturday, March 27th at 11 PM.

• I will be out of town for part of this week; please see below for necessary adjustments.

• No Office Hours on Tuesday this week (in view of my travel).

Tuesday, March 24th

• No Class (compensation for evening exam).

Thursday, March 25th

• Review for Midterm 1.

Week of March 30th (Week 12)

• Midterm 2 is on Monday, March 30th from 8:00 PM to 9:00 PM in LWSN B155.

• Extra Office Hours on M, 4:00 PM to 6:00 PM this week (in addition to usual Office Hours) in view of Midterm 2.

Tuesday, March 31st

• HW 10 is due on Saturday, April 3rd at 11 PM.

• Reading: §3.3 Linear Fractional Transformations.

Thursday, April 1st

• Reading: §3.3 Linear Fractional Transformations.

Week of April 6th (Week 13)

• HW 11 is due on Saturday, April 11th at 11 PM.

Tuesday, April 7th

• Reading: §3.4 Conformal Mapping.

Thursday, April 9th

• Reading: §3.4 Conformal Mapping.

Week of April 13th (Week 14)

• HW 12 is due on Saturday, April 18th at 11 PM.

• I will be out of town for part of this week; please see below for necessary adjustments.

• No Office Hours on Tuesday this week (in view of my travel).

Tuesday, April 14th

• No Class (compensation for evening exam).

Thursday, April 16th

• Reading: TBA (assorted applications or special topics).

Week of April 20th (Week 15)

• HW 13 is due on Saturday, April 25th at 11 PM.

Tuesday, April 21st

• Reading: TBA (assorted applications or special topics).

Thursday, April 23rd

• Reading: TBA (assorted applications or special topics).

Week of April 27th (Week 16)

• No HW due this week (in view of Quiet Period).

Tuesday, April 28th

• Review for Final Exam.

Thursday, April 30th

• Review for Final Exam.

Week of May 4th (Final Exam Week)

• Final Exam schedule TBA by Registrar.