 Pravděpodobně máte vypnutý JavaScript. Některé funkce portálu nebudou funkční.
Course detail
Partial Differential Equations
Course unit code:  FSISPD  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Bachelor's (1st cycle)  
Year of study:  3  
Semester:  winter  
Number of ECTS credits:  5  



























Type of course unit:
Lecture:  26 hours, optionally 

Teacher / Lecturer:  prof. RNDr. Jan Franců, CSc. 
Syllabus:  1 Revision of O.D.E.  1st order equations and higher order linear equations. 2 Systems of linear O.D.E., stability, existence and uniqueness of the solution. 3 Autonomous systems, trajectories and classification of singular trajectories. 4 Elements of P.D.E., 1st order equations. 5 The Cauchy problem, classification of 2nd order equations. 6 Derivation of selected equations of mathematical physics: heat equation. 7 Derivation of the equation of string vibration, wave equations. 8 Derivation of membrane equation via variational principle. 9 Method of characteristics for 1D wave equation. 10 Fourier series method. 11 Integral transform method. 12 Green function method and the maximum principles. 13 Properties of the solutions, reserve. 
seminars:  26 hours, compulsory 
Teacher / Lecturer:  prof. RNDr. Jan Franců, CSc. 
Syllabus:  1 O.D.E., solution of the 1st order equations and higher order linear equations. 2 Solution of systems of linear O.D.E., stability of the solution. 3 The phase portrait of solutions to autonomous system. 4 P.D.E., solving of the 1st order equations. 5 Written test 1, classification of 2nd order equations. 6 Formulation of problems related to the heat equation. 7 Formulation of problems related to the wave equation. 8 Derivation of membrane equation via variational principle. 9 Solving problems by the method of characteristics. 10 Solving problems by the Fourier series method. 11 Written test 2. 12 Using the Green function method, harmonic functions. 13 Properties of the solutions, coursecredits. 