(I reserve the right to permute the order of the topics.)

Complex numbers. Limits. Continuity. Differentiability. Analytic functions. Elementary functions. Real integrals of complex functions. (4 hours)

Complex integrals. Cauchy’s integral theorem. Cauchy’s integral formula. (4 hours)

Trigonometric polynomials. Approximation by trigonometric polynomials. Fourier series. Discrete Fourier transform. (8 hours)

Series of real and complex functions. Convergence tests. Taylor, McLaurin, Laurent

series. Properties of zeros and poles. (5 hours)

Sequence spaces. The z-transform and its inverse. Discrete linear systems and

filters. Convolution. Frequency analysis. Special purpose filters. (7 hours)

Improper integrals. Continuous linear systems and filters. Integration by the method

of residues. Laplace and Fourier transforms and their inverses. Frequency analysis.

Special purpose filters. (8 hours)