Course Code MCC203
Semester 3
Category Basic
Points 4
ECTS Units 7
Recommended Reading

1. Farlow, S.J., “ Partial Differential Equations for Scientists and Engineers”, Dover,1993.

2. Sokolnikoff, I.S, και Redheffer, R.M., “Mathematics in Physics and Modern Engineering”, McGraw Hill, New York 1966.

3. Tikhonov, A.N. και Samarskii, A.A., “ Equations of Mathematical Physics”, Dover, New York 1990.

Course Description

Partial Differential Equations –  Fourier Series–Fourier Integral–

Fourier Transforms– Complex Analysis :

1. Basic definitions.

2. The one-dimensional wave equation.

3. Transverse oscillations of an elastic membrane.

4. Heat flow in a specific direction.

5. Continuity equation.

6. The method of separation of variables.

7.  The wave equations in polar and spherical system of coordinates.

8. The eigenvalue problem Ly=λy.  The theorem of Sturm-Liouville.

9. Laplace equation in Cartesian, polar, cylindrical and spherical system of coordinates. Dirichlet’s problem.

10. Fourier Series. Fourier Integral. Applications.

11. Wave propagation along an elastic chord of infinite length.

12. Poisson equation. Helmholtz equation.

13. Fourier Transforms.

14. Complex numbers.

15. Complex functions.

16. Derivative of complex function.

17. Complex integration.

18. Integral types of Cauchy and theorems.

19 Taylor-Laurent Series and Integral residuals.

20. Conformal mapping