| Date | Section and Topic | Read before class | Homework |
| January 17 | Organization and introduction | Section 1.1 | HW 1 due Jan 24: 1.1: 1, 7, 17, 20, 23; 1.2: 6, 7, 10, 14, 17 |
| January 19 | What are complex numbers, really? | Section 1.2 | |
| January 22 | Polar form of complex numbers | Section 1.3 | January 24 | Complex exponential | Section 1.4 | HW 2 due Jan 31: 1.3: 6, 7, 8, 12, 17; 1.4, 1, 3, 5, 7, 13, 16, 19; 1.5: 2, 4, 5, 7, 10. |
| January 26 | Roots and powers | Section 1.5 | |
| January 29 | Planar Sets | Section 1.6 | |
| January 31 | The Riemann Sphere | Section 1.7 | HW 3 due Feb. 7: 1.6: 2-8, 10, 13, 17; 1.7: 1, 2, 5, 6. |
| February 2 | More on the Riemann Sphere | ||
| February 5 | Functions of a complex variable, limits of sequences | Sections 2.1, 2.2 | |
| February 7 | Limits of functions, continuity, analyticity | Section 2.3 | HW 4 due Feb 14: 2.1: 1, 4, 5, 10, 17; 2.2: 3, 7, 11, 12, 23; 2.3: 2, 3, 4, 7, (read 8), 15 |
| February 9 | Analyticity, Cauchy-Riemann equations | Section 2.4 | |
| February 12 | More on Cauchy-Riemann, Harmonic functions | Section 2.5 | |
| February 14 | Harmonic functions, review | ||
| February 16 | Exam 1 | Chapters 1 and 2 | |
| February 19 | Polynomial functions | Section 3.1 | HW 5 due Feb 21: Test corrections |
| February 21 | Rational functions, Exponential function | Section 3.1, 3.2 | HW 6 due Feb 28: 2.4: 1, 3, 4, 8, 16; 2.5 1,3,7, 11, 14; 3.1: 1, 7, 10, 15 |
| February 23 | Trig and hyperbolic functions | Section 3.2 | |
| February 26 | Logarithmic function | Section 3.3 | |
| February 28 | Complex powers | Section 3.5 | HW 7 due Mar 7: 3.2: 4, 5, 7, 9, 18; 3.3: 1, 3, 5, 6, 7, 9, 11, 16; 3.5: 1, 3, 4, 5, 6, 11, 15. |
| March 2 | Contours | Section 4.1 | |
| March 5 | Contour integrals | Section 4.2 | |
| March 7 | More on contour integrals | Section 4.2 | HW 8 due Mar 14: 4.1: 1, 3, 4, 7, 8, 10, 11; 4.2: 3, 5, 7, 8, 10, 11, 14; 4.3: 1, 2. |
| March 9 | Independence of Path | Sections 4.3 | |
| March 12 | Cauchy's integral theorem | Sect 4.4 B (no need to read part A!) | |
| March 14 | Cauchy's integral formula | Sect 4.5 | HW 9 due Mar 21: 4.4: 9, 10, 13, 15, 16, 18, (read 19); 4.5: 2, 3, 4, 5, 6, 9, 11; 4.6: 4, 5, 6, 13, 14, 17. |
| March 16 | More on Cauchy's integral formula | Sect 4.5 | |
| March 19 | Louiville's Theorem, Fund Thm of Algebra | Sect 4.6 | |
| March 21 | Maximum modulus principle | Sect 4.6 | |
| March 23 | Exam 2 | Sect 3.1-3.3, 3.5, 4.1-4.6 | |
| April 2 | Series | Sect 5.1 | HW 10: Due April 11: 5.1: 1-7, 9, 11; 5.2: 1-5, 8, 13; 5.3: 2, 3, 5, 6, 8, 11, 14, 18 |
| April 4 | Taylor Series | Sect 5.2 | |
| April 6 | Power Series | Sect 5.3 | |
| April 9 | More on power series | ||
| April 11 | Laurent series | Sect 5.5 | HW 11 due April 18: 5.5: 1, 4, 6, 7, 5.6: 1, 2, 3, 5, 6, 12 |
| April 13 | Zeroes and poles | Sect 5.6 | |
| April 16 | The residue theorem | Sect 6.1 | |
| April 18 | Trig Integrals over [0, 2 pi] | Sect 6.2 | HW 12 due April 25: 6.1: 1, 3, 4; 6.2: 1, 2, 5; 6.3: 1, 2, 15 (I'll do 14 in class); 6.4: 1, 2. |
| April 20 | Improper integrals over the real line | Sect 6.3 | |
| April 23 | Improper integrals with trig functions | Sect 6.4 | |
| April 25 | Indented Contours | Sect 6.5 | HW 13: Due May 2: 6.5: 1, 2, 5; 6.7: 1, 2, 3, 4, 6, 7. |
| April 27 | Argument principle | Sect 6.7 | |
| April 30 | Rouche's Theorem | Sect 6.7 | |
| May 2 | Review | ||
| May 9 | Final Exam: 1:30-4 pm | Chapters 1-6 |