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Course detail
Mathematics III
Course unit code:  FSI3M  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Bachelor's (1st cycle)  
Year of study:  1, 2  
Semester:  winter  
Number of ECTS credits:  8  



























Type of course unit:
Lecture:  39 hours, optionally 

Teacher / Lecturer:  doc. Mgr. Zdeněk Opluštil, Ph.D. doc. Ing. Jiří Šremr, Ph.D. doc. Ing. Petr Tomášek, Ph.D. 
Syllabus:  1. Number series. Convergence criteria. Absolute and nonabsolute convergence. 2. Function and power series. Types of the convergence and basic properties. 3. Taylor series and expansions of functions into Taylor series. 4. Fourier series. Problems of the convergence and expansions of functions. 5. ODE. Basic notions. Analytical methods of solving of 1st order ODE. The existence and uniqueness of solutions. 6. Higher order ODEs. Properties of solutions and methods of solving of higher order homogeneous linear ODEs. 7. Properties of solutions and methods of solving of higher order nonhomogeneous linear ODEs. 8. Laplace transform and its use in solving of linear ODEs. 9. Systems of 1st order ODEs. Properties of solutions and methods of solving of homogeneous linear systems of 1st order ODEs. 10. Properties of solutions and methods of solving of nonhomogeneous linear systems of 1st order ODEs. 11. Stability of solutions of ODEs. Boundary value problem for 2nd order ODEs. 12. PDEs. Basic notions. 13. Classification of 2nd order PDEs and basic methods of solving. 
seminars:  39 hours, compulsory 
Teacher / Lecturer:  RNDr. Rudolf Hlavička, CSc. Ing. Tomáš Kisela, Ph.D. RNDr. Karel Mikulášek, Ph.D. Mgr. Aleš Návrat, Ph.D. doc. Ing. Luděk Nechvátal, Ph.D. doc. Mgr. Zdeněk Opluštil, Ph.D. Mgr. Jan Pavlík, Ph.D. András Rontó doc. Ing. Jiří Šremr, Ph.D. doc. Ing. Pavel Štarha, Ph.D. doc. Ing. Petr Tomášek, Ph.D. Mgr. Petr Vašík, Ph.D. Mgr. Jitka Zatočilová, Ph.D. doc. RNDr. Libor Žák, Ph.D. 
Syllabus:  1. Limits and integrals  revision. 2. Infinite series. 3. Function and power series. 4. Taylor series. 5. Fourier series. 6. Analytical methods of solving of 1st order ODEs. 7. Analytical methods of solving of 1st order ODEs (continuation). 8. Higher order linear homogeneous ODEs. 9. Higher order nonhomogeneous linear ODEs. 10. Laplace transform method of solving of linear ODEs. 11. Systems of 1st order linear homogeneous ODEs. 12. Systems of 1st order linear nonhomogeneous ODEs. 13. Fourier method of solving of PDEs. 
seminars in computer labs:  13 hours, compulsory 
Teacher / Lecturer:  Mgr. Monika Dosoudilová, Ph.D. RNDr. Rudolf Hlavička, CSc. doc. Mgr. Zdeněk Opluštil, Ph.D. Mgr. Jan Pavlík, Ph.D. Ing. Pavla Sehnalová, Ph.D. Mgr. Viera Štoudková Růžičková, Ph.D. Ing. Jan Šútora Mgr. Jitka Zatočilová, Ph.D. doc. RNDr. Libor Žák, Ph.D. 
Syllabus:  The course is realized in computer labs. The MAPLE software is utilized to illustrate and complete the following topics: 1. Revision of basic skills in MAPLE. 2. Function series  graphical illustrations of types of the convergence (with a special emphasize on Taylor and Fourier series). 3. 1st order ODEs  geometrical interpretation of solutions, graphical methods of solving (direction fields). 4. 1st order ODEs  applications (orthogonal trajectories and others). 5. Higher order ODEs  graphical interpretations of solutions, Taylor series method. 6. Systems of 1st order ODEs  graphical interpretations of solutions, the phase portrait. 7. PDEs  selected methods of solving. 