| 1 | Complex plane and basic definitions of complex variables, derivative of a complex function and complex analiticity, Cauchy-Riemann equations | [1] pp.113-129; [2] pp.83-90; |
| 2 | Multiple-valued complex functions, Residue theorem, Cauchy integral theorem | [1] pp.113-128; [2] pp.83-90; [21] pp.149-159; |
| 3 | Line integral on the complex plane and applications | [1] pp. 129-138; [4] pp. 455-487; |
| 4 | Taylor and Laurent series, Poisson integral formulas | [1] pp. 143-148; [7] pp. 43-44; |
| 5 | Integral representations of Gamma and Beta functions | [7] pp. 94-98; [6] pp. 499-533; |
| 6 | Saddle point method, Mittag-Leffler expansion | [7] pp. 87-93; [7] pp. 84-86; [2] pp. 90-107; |
| 7 | Introduction to conformal transformations and application to static electricity in two dimensions | [2]pp. 90-114; [4] pp. 216-228; |
| 8 | Fourier series and Fourier transform | [1] pp.169-182; [4] pp. 193-215; |
| 9 | Properties and applications of Fourier transform | [1]pp. 183-189; [2] pp. 189-201; |
| 10 | Laplace transform and properties | [1] pp.189-192; [6] pp. 931-951; |
| 11 | Inverse Laplace transform and Bromwich integral; Applications of Laplace transform to differential equations | [1] pp.192-204; [6]pp.951-961; |
| 12 | Variational methods and applications (three weeks) | [2]pp. 223-247; [2]pp. 235-290. |