Course aims:

Modelling and solving some medium complexity level problems, using the mathematical and engeneering sciences knoweledges.
To be able to predict the systems behavior in other circumstances. The learning integrates theory and application using a problem-based approach. This will relieve the student of performing, by hand, many of the detailed calculations needed.
Prepares the student for future learning in relation to problem solving and decision-making; technical competence; teamwork and leadership; and reflection.

Course Entry Requirements:

Linear Algebra, Mathematical Analysis

Course contents:

CAP. I DIFFERENTIAL EQUATIONS 1. First order differential equations 2. Differential equations of higher order 3. Systems of linear differential equations; Systems of linear differential equations with constant coefficients 4. Partial differential equations of the first order linear; Partial differential equations of the second order - the equations of mathematical physics. CAP. II ELEMENTS OF THE THEORY OF FIELDS 5. Scalar field; vector field 6. Divergence and rotor of a vector field; Hamilton's operator. CAP. III FUNCTIONS OF A COMPLEX VARIABLE COMPLEX 7. Complex numbers. geometrical interpretation 8. Functions of a complex variable 9. Derivative of a complex function of a complex variable: Cauchy-Riemann conditions; analytical function 10. Advanced functions Elementary CAP. IV PROBABILITY AND STATISTICS 11. Random variables; Field of probabilities, conditional probabilities 12. Laws classical probability 13. Functions distributions, probability density 14. Representations of statistical distributions

Teaching methods:

Lecture, conversation, exemplification.

Learning outcomes:

Modelling and solving some medium complexity level problems, using the mathematical and engeneering sciences knoweledges.

Learning outcomes verification and assessment criteria:

Written paper 50%; mid-term test 30%; seminar activities 20%.

Recommended reading:

• Peter V. O’Neil, Advanced Engineering Mathematics, Thomson, 2007
• Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons Inc. 9th Edition, 2006.
• D. G. Zill, M.R. Cullen, Differential Equations with Boundary Problems, 6th Edition, Brooks/Cole Publishing Company, 2005.
• Lisei, H., Micula, S., Soos, A., Probability Theory trough Problems and Applications, Cluj University Press, 2006.
• Milton, J.S., Arnold, J. C., Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, McGraw-Hill, New York, 1995.