Course title  Mathematics 3 

Course code  KMA/M3 
Organizational form of instruction  Lecture + Exercise 
Level of course  Bachelor 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  3 
Language of instruction  Czech 
Status of course  Compulsory 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
ORDINARY DIFFERENTIAL EQUATIONS (ODEs) 1. Introduction. Motivation. 2. First order ODEs, Cauchy initial problem, existence and uniqueness of solutions, direction field. 3. Elementary methods: separable ODEs. 4. Elementary methods: substitutions. 5. Linear first order ODEs, Method of variation of parameters. 6. Linear second order ODEs. 7. Homogeneous linear second order ODEs. 8. Nonhomogeneous linear second order ODEs: method of variation of parameters. 9. Nonhomogeneous linear second order ODEs: method of variation of undetermined coefficients. DIFFERENCE EQUATIONS 10. First order difference equations, linear first order difference equations. 11. Linear nth order difference equations: homogeneous equations with constant coefficients. 12. Linear nth order difference equations: nonhomogeneous equations with constant coefficients  method of undetermined coefficients.

Learning activities and teaching methods 
Monologic Lecture(Interpretation, Training)

Learning outcomes 
Basic skills in the treatment of ordinary differential and difference equations.
Comprehension Basic skills in the treatment of ordinary differential and difference equations. 
Prerequisites 
Differential calculus of functions of one and several variables, integration on the real axis.
KMA/M2  or  KMA/M2N 
Assessment methods and criteria 
Mark, Oral exam, Written exam
Credit: the student has to obtain at least half of the possible points in written test. Exam: the student has to understand the subject. 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 

Faculty of Science  Applied Statistics (2015)  Mathematics courses  2  Winter 
Faculty of Science  MathematicsEconomics of Banking / Insurance Systems (1)  Mathematics courses  2  Winter 