Objective: evaluation of a real integrals of the form: 00 [F(@)cos@ada and 8 [F(@)sinwada occurring in a connection with the Fourier Integral in conjunction with the Characteristic Function and the Wiener - Khintchine Theorem in Random Processes. Project: Evaluate using the: a) Analytical Technique (using the Cauchy Residue Theorem). b) Computer simulation (use the existing subroutines- for example: Maple) +80 cos wada e +80 jan dw 2. 1. 2 1 + @ 800 a² + w² +2 +00 cos wadw 3. (a² + w²)² e-jaw dw 4. 8 -00 (a²+w²) (ẞ²+w²) The topics which should be included in this project for a better understanding of this subject should include: 1. Complex analytics functions: Cauchy-Riemann equations + examples. C2. Complex integrals: line integral, Cauchy's integral Theorem and Formula 3. Power series, Taylor series, Laurent series, and examples. 4. Integration by the Method of Residues: the residue theorem and the evaluation Dyal of a real integrals and examples.