Module also offered within study programmes:
General information:
Name:
Mathematical modeling
Course of study:
2017/2018
Code:
STC-2-117-CF-s
Faculty of:
Energy and Fuels
Study level:
Second-cycle studies
Specialty:
Clean Fossil and Alternative Fuels Energy
Field of study:
Chemical Technology
Semester:
1
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
dr Jarnicka Jolanta (jarnicka@wms.mat.agh.edu.pl)
Academic teachers:
dr Jarnicka Jolanta (jarnicka@wms.mat.agh.edu.pl)
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 Student is able to indicate the relations between energy - economy - environment in the fuels and energy systems. TC2A_K01 Activity during classes
Skills
M_U001 Student is able to define relevant elements of the systems, their relations and note them in the mathematical formulas Test
Knowledge
M_W001 Student is able to describe the typical structure of the model and can identify the main elements with their relations that occur in real fuel and energy systems. TC2A_W01 Test
M_W002 Has knowledge of multi-variable differential calculus; knows how to find local and conditional extremas TC2A_W04 Test
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Social competence
M_K001 Student is able to indicate the relations between energy - economy - environment in the fuels and energy systems. - - - - - - - - - - -
Skills
M_U001 Student is able to define relevant elements of the systems, their relations and note them in the mathematical formulas - + - - - - - - - - -
Knowledge
M_W001 Student is able to describe the typical structure of the model and can identify the main elements with their relations that occur in real fuel and energy systems. + - - - - - - - - - -
M_W002 Has knowledge of multi-variable differential calculus; knows how to find local and conditional extremas - - - - - - - - - - -
Module content
Lectures:

Elements of vector analysis, basic operations on vectors,
differentiation of vectors, curvilinear coordinate systems. Integral
transformations: Fourier transform, Laplace transform, the use of
operator. The calculus of variations: The term functional. Extreme
functional. Variation functional. Euler’s equation. Functional
dependent on many variables f. Ritz method. Ordinary differential
equations, differential equations of the order of 1 – review,
differential equations of order 2 – review, systems of differential
equations, bringing equations of higher orders to the system of
equations row 1st, issue of the stability of solutions. Partial
differential equations, classification of partial differential
equations of order 2, the method of separation of variables, the use
of integral transformation, the heat equation. Special methods for
solving initial-boundary issues.

Auditorium classes:

1. Expanding functions into Fourier series, special cases of odd and even functions
2. The Fourier and Laplace transform
3. Solving differential equations of the 1st order
4. Solving linear differential equations of higher order
5. Differential calculus of the multiple variable functions
6. Building models to solve simple problems.
7. 2. class test

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 108 h
Module ECTS credits 4 ECTS
Participation in lectures 28 h
Participation in auditorium classes 28 h
Examination or Final test 2 h
Preparation for classes 50 h
Additional information
Method of calculating the final grade:

Grading:
Grading formula: FG= PMWFftest *PMGftes+ PMWFdmodel * PMGdmode
Where:
• FG-final grade
• PMWFftest – final test part weighting factor – 0,5
• PMGftest– Grade of achieved LOs relevant to final test
• PMWFdmodel – designing of the model part weighting factor – 0,5
• PMGdmode – Grade of achieved LOs relevant to designing of the model

All LO weighting factors associated with part of the module (PM) equal 1.

Prerequisites and additional requirements:

No special requirements

Recommended literature and teaching resources:

1. J. Bird “Higher Engineering Mathematics”
2. B. Demidovitch “Problems in Mathematical Analysis”
3. W. F. Trench “Elementary Differential Equations”
abys W. C., Modeling Mineral and Energy Markets, Kluwer Academic Publishers, Boston. 1999
Thompson G.L, Thore S, Computational economics, SC Press 1992
Systems modeling for energy policy, 1997, Ed. Bunn D.W., Larsen E.R., John Wiley and Sons

McCarl B.A., Spreen T.H., 1997, Applied mathematical programming using algebraic methods, http://agecon2.tamu.edu/people/faculty/mccarl-bruce/mccspr/thebook.pdf ,

Scientific publications of module course instructors related to the topic of the module:

Additional scientific publications not specified

Additional information:

The overall assessment consist of two steps:
1. Assessment of fulfilling of module learning outcomes and OLOs.
2. Assessment and grading of the quality of students work.
EIT OLOs assessed in the industrial internship:
• Making value judgments and sustainability competencies (EIT OLO 1)
• Entrepreneurship skills and competencies (EIT OLO 2)
• Creativity skills and competencies (EIT OLO 3)
• Innovation skills and competencies (EIT OLO 4)
• Research skills and competencies (EIT OLO 5)
• Intellectual transforming skills and competencies (EIT OLO 6)
• Leadership skills and competencies (EIT OLO 7)
The Method of assessments indicated in point description of learning outcomes for modulen icludes
assessment of learning outcomes and OLOs