Lecture Notes

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
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
17 Radius of Convergence of Taylor Series (PDF)
III. Residue Calculus
21 Real Integrals From -∞ to +∞

Conversion to cx Contours
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
32 Questions of Convergence

Scanning Function

Gibbs Phenomenon
35 Special Topic: The Magic of FFTs I (PDF)
36 Special Topic: The Magic of FFTs II (PDF)