The subject is focused on the development of the mathematical models of important physical and chemical processes occurring in materials. The models are developed using the approach based on experimental design in combination with regression analysis. Emphasis is put on detailed statistical analysis of experimental data and the developed models. The models are used for the optimization of the composition of materials with target properties. By applying numerical methods, physic-chemical processes are solved that are described by ordinary and partial differential equations.

Students will be able to:

Plan experimental design and data analysis

Develop mathematical models for materials’ properties and optimizing materials’ composition

Numerically solve ordinary and partial differential equations

R:Meloun M., Militký J.: Statistická analýza experimentálních dat, Academia, 2004, ISBN: 8020012540

R:Urbánek T., Škárka J.: Microsoft Excel 97 pro vědce a inženýry, Computer press, 1998, ISBN: 8072260995

A:Cornell J.A.: Experiments With Mixtures, John Wiley, 1981, ISBN: 0471079162

A:Jarník V.: Diferenciální počet (I), Academia, 1974, ISBN: 2110174

A:Jarník V.: Integrální počet (I), Academia, 1974, ISBN: 2110874

Microsoft Excel, www.microsoft.com

1. Overview of mathematical software for advanced applications in chemical engineering.

2. Experimental design.

3. Statistical analysis of data.

4. Regression analysis and fitting of models.

5. Statistical analysis of models, standard error, R square, t- and F-statistics, testing of hypothesis.

6. Calculation of materials’ properties from chemical composition. Composition optimization.

7. Numerical methods of derivation and integration.

8. Numerical solving of ordinary differential equations with initial value.

9. Numerical solving of ordinary differential equations - boundary problem.

10.Numerical solving of partial differential equations by finite differences method.

11.Numerical solving of heat transfer in glass and ceramics.

12.Numerical solving of mass transfer in glass and ceramics.

13.Numerical solving of wave function.

14.Individual project.

1. Overview of mathematical software for advanced applications in chemical engineering.

2. Experimental design.

3. Statistical analysis of data.

4. Regression analysis and fitting of models.

5. Statistical analysis of models, standard error, R square, t- and F-statistics, testing of hypothesis.

6. Calculation of materials’ properties from chemical composition. Composition optimization.

7. Numerical methods of derivation and integration.

8. Numerical solving of ordinary differential equations with initial value.

9. Numerical solving of ordinary differential equations - boundary problem.

10.Numerical solving of partial differential equations by finite differences method.

11.Numerical solving of heat transfer in glass and ceramics.

12.Numerical solving of mass transfer in glass and ceramics.

13.Numerical solving of wave function.

14.Individual project.