714-0913/01 – Mathematical Methods in Transport Phenomena (MMPJ)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantordoc. RNDr. Věra Dobrovská, CSc.Subject version guarantordoc. RNDr. Věra Dobrovská, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1997/1998Year of cancellation2011/2012
Intended for the facultiesFMTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOB40 doc. RNDr. Věra Dobrovská, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 28+0

Subject aims expressed by acquired skills and competences

Main study goals: -to be acquainted with actual progress in this mathematical discipline, -to extend needed theoretical knowledge with emphasized orientation to its applicability, -to increase communication ability of specialists in different branches. With regard to professional orientation of students learning themes modification is offered to fulfill presented aims.

Teaching methods

Lectures
Individual consultations

Summary

The course includes the selected chapters on tensor calculus, a field theory and the solution methods of boundary value problems for both ordinary and partial differential equations. Acquired knowledge can be used in mathematical modelling of heat, mass and momentum transfer.

Compulsory literature:

Farrashkhalvat,J.P.: Tensor methods for engineers. Publ. Ellis Horwood, New York, London 1990. Bick,T.A.: Elementary boundary value problems. Marcel Dekker, New York 1993. Crank,J.: The mathematics of diffusion. Oxford University Press, 1975. Carrier,G.F., Pearson,C.E.:Partial differential equations, theory and technique. Academia press, Boston 1988. Bird,R.B.,Stewart,W.E.,Lightfoot,E.N.: Transport phenomena. John Wiley & Sons, New York 1965.

Recommended literature:

Poirier,D.R., Geiger,G.H.: Transport Phenomena in Materials Processing. The Minerals, Metals and Materials Society, 1994

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Tensors calculus. Tensors of the first and the second orders. Operations, properties, differential operations. 2. Theory of field Scalar and vector fields. Integral theorems: Stokes and Gauss-Ostogradski’s. Differential operators in curvilinear orthogonal coordinates. Application: Equation of continuity. Heat, mass and momentum transfer. 3. Boundary value problems for ordinary differential equations Boundary value problem formulation. Orthogonal systems of functions. Fourier series. Sturm-Liouville’s problem. The methods of homogeneous and nonhomogeneous boundary value problem solutions. Application: Stationary conduction of heat and diffusion in plane sheet, cylinder and sphere. 4. Boundary value problems for partial differential equations Linear partial differential equations of the second order and their classification. Boundary conditions. Boundary value problem formulation. The methods of boundary value problem solutions. 5. The methods of parabolic equations solution Method of separation of variables, method of similarity transformation, method of Green’s function, finite-difference method. Application: Nonstationary heat conduction and diffusion in plane sheet, cylinder and sphere. Nonstationary heat conduction and diffusion in bodies of finite dimensions. 6. The methods of elliptic equations solution Method of separation of variables, method of analytic functions, finite-difference method. Application: Stationary models of two-dimensional diffusion and two-dimensional heat conduction. 7. The methods of hyperbolic equations solution Method of characteristic, method of separation of variables, finite-difference method.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2009/2010 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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2010/2011 (P2106) Metallurgy (2109V037) Thermal Engineering and Fuels in Industry K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2106) Metallurgy (2807V003) Chemical Metallurgy K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
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2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2009/2010 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2009/2010 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2106) Metallurgy (2109V036) Metallurgical Technology P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2106) Metallurgy (2109V037) Thermal Engineering and Fuels in Industry P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2106) Metallurgy (2807V003) Chemical Metallurgy P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2106) Metallurgy (2109V036) Metallurgical Technology K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2106) Metallurgy (2109V037) Thermal Engineering and Fuels in Industry K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2106) Metallurgy (2807V003) Chemical Metallurgy K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
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2007/2008 (P3924) Materials Science and Engineering (3911V999) Fyzikální metaluirgie a mezní stavy materiálů K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (P3924) Materials Science and Engineering (3911V888) Materiálové inženýrství P Czech Ostrava Choice-compulsory study plan
2006/2007 (P3924) Materials Science and Engineering (3911V999) Fyzikální metaluirgie a mezní stavy materiálů P Czech Ostrava Choice-compulsory study plan
2006/2007 (P3924) Materials Science and Engineering (3911V888) Materiálové inženýrství K Czech Ostrava Choice-compulsory study plan
2006/2007 (P3924) Materials Science and Engineering (3911V999) Fyzikální metaluirgie a mezní stavy materiálů K Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan

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