Objective: evaluation of a real integrals of the form: [F(@)coswoda and 88 F(@)sin@oda 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) +00 J e jae d@ 2. 2 1 + @ 88 cos wada 3. (a² + w²)² cos a cos wadw a² + w² e-jaw dw 4. So (a²+w²) (B²+w²) 8 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. 2. 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 of a real integrals and examples.