| 1 | 1 | 1.1 Complex Algebra. Complex Plane. Motivation and History | |
| 2 | 1.2 Polar Form. Complex Exponential. DeMoivre's Theorem | |
| 3 | 1.3 Newton's Method. Fractals | |
| 2-3 | 4 | 2.1 Complex Functions. Analyticity | |
| 5 | 2.2 Cauchy-Riemann Eqns. Harmonic Functions | |
| 6 | 2.3 Exponential and Trig. Functions. Logarithmic Function | |
| 7 | 2.4 Branch Cuts. Applications | |
| 8 | 2.5 Complex Powers and Inverse Trig. Functions | |
| 4-5 | 9 | 3.1 Contour Integrals | |
| 10 | 3.2 Path Independence | |
| 11 | 3.3 Cauchy's Theorem | |
| 12 | 3.4 Cauchy's Integral Formula | |
| 13 | 3.5 Liuville's Theorem. Mean Value and Max. Modulus | |
| 14 | 3.6 Dirichlet Problem | |
| 15 | | EXAM #1: covering 1, 2 and about 1/2 of 3. |
| 6 | 16 | 4.1 Taylor Series. Radius of Convergence | |
| 17 | 4.2 Laurent Series | |
| 18 | 4.3 Zeros. Singularities. Point at Infinity | |
| 7-8 | 19 | 5.1 Residue Theorem. Integrals over the Unit Circle | |
| 20 | 5.2 Real Integrals. Conversion to Complex Contours | |
| 21 | 5.3 Trig. Integrals. Jordan's Lemma | |
| 22 | 5.4 Indented Contours. Principal Value | |
| 23 | 5.5 Integrals Involving Multi-valued Functions | |
| 24 | 5.6 Argument Principle and Rouche's Theorem | |
| 25 | | EXAM #2: covering second half of 3, 4 and 5. |
| 9-10 | 26 | 6.1 Complex Fourier Series | |
| 27 | 6.2 Oscillating Systems. Periodic Functions | |
| 28 | 6.3 Applications of Fourier Series | |
| 29 | 6.4 Fourier Transform and Applications | |
| 30 | 6.5 Laplace Transform and Inversion Formula | |
| 11-12 | 31 | 7.1 Invariance of Laplace's Eqn. Conformality | |
| 32 | 7.2 Inversion Mapping. Bilinear Mappings | |
| 33 | 7.3 Examples and Applications | |
| 34 | 7.4 More Examples (if time permits) | |
| 35 | | EXAM #3: covering 6 and 7. |