Aims of this course are to:

1. Teach students how to mathematically model engineering systems, provide students with a systematic understanding of core areas and topics in mathematical simulation;
2. Teach students how to use computer tools to solve the resulting mathematical models of problems encountered in mechanical engineering;
3. Develop students’ skills in using modern engineering tools and relate the usage to simulation of systems in mechanical engineering.

Course objectives can be structured as follows:

1. to introduce the key types of mathematical models for solving real-world problems;
2. to give students practice in synthesizing mathematical models, in interpreting the results of mathematical models;
3. to alert students to the non-mathematical constraints under which mathematicians operate in the industrial environment;
4. to give practice in critically examining the various possible approaches to, and models of, a system, and choosing an optimal method of simulation within the constraints of the environment;
5. to demonstrate the range of problems that are modeled mathematically, and illustrate the scope of the engineering tasks;
6. to give students practice in evaluating the effects of the various sections of, and inputs to, models, and making appropriate simplifications and approximations to aid efficient solution.

Topics for individual research:

1. Methods of forecasting time series values;
2. Auto-covariance and autocorrelation.
3. Multiple regression analysis.
4. Non-linear regression.
5. Optimal placement of production facilities

References

Basic

• M. Meerschaert, Mathematical Modeling / M. M. Meerschaert. — Second edition. — San Di-ego: Academic Press, 1999. — 351 p.
• B. T. Kulakowski, Dynamic Modeling and Control of Engineering Systems / B. T. Kulakowski, J. F. Gardner, J. L. Shearer. — Third Edition. — New York: Cambridge University Press, 2007. — 486 p.
• Rao, S.S., Applied Numerical Methods for Engineers and Scientists, Prentice Hall, Upper Sad-dle River, New Jersey, NJ, 2002.

Additional

• K.Velten, Mathematical Modeling and Simulation/ K.Velten. – New York: Wiley, 2008. – 362 p.
• D. Mooney, R. Swift, A Course in Mathematical Modeling / Douglas D. Mooney, Randall Swift. – Cambridge: Cambridge University Press, 1999. – 452p.