Our supplementary handouts were mostly graphical, and they appeared at the lectures listed in this table.
| I. Complex Algebra and Functions |
| 5 |
Simple Mappings: az+b, z2, √z
Idea of Conformality |
(PDF) |
| 6 |
Complex Exponential |
(PDF) |
| 7 |
Complex Trigonometric and Hyperbolic Functions |
(PDF) |
| II. Complex Integration |
| 11 |
Contour Integrals |
(PDF) |
| 15 |
Bounds
Liouville's Theorem
Maximum Modulus Principle |
(PDF) |
| 17 |
Radius of Convergence of Taylor Series |
(PDF) |
| III. Residue Calculus |
| 21 |
Real Integrals From -∞ to +∞
Conversion to cx Contours |
(PDF) |
| IV. Conformal Mapping |
| 25 |
Invariance of Laplace's Equation |
(PDF) |
| 27 |
Bilinear/Mobius Transformations |
(PDF) |
| 28 |
Applications I |
(PDF) |
| 29 |
Applications II |
(PDF) |
| V. Fourier Series and Transforms |
| 30 |
Complex Fourier Series |
(PDF) |
| 31 |
Oscillating Systems
Periodic Functions |
(PDF) |
| 32 |
Questions of Convergence
Scanning Function
Gibbs Phenomenon |
(PDF) |
| 35 |
Special Topic: The Magic of FFTs I |
(PDF) |
| 36 |
Special Topic: The Magic of FFTs II |
(PDF) |