Mathematics 4
Code  Completion  Credits  Range  Language 

01MAT4  Z,ZK  4  2+2  Czech 
 Vztahy:
 In order to register for the course 01MAT4, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 01MAT2. The course 01MAT4 can be graded only after the course 01MAT2 has been successfully completed.
 The course 01MAT4 can be graded only after the course 01MAT2 has been successfully completed.
 Garant předmětu:
 Matěj Tušek
 Lecturer:
 Matěj Tušek
 Tutor:
 Lukáš Heriban, David Kramár, Matěj Tušek
 Supervisor:
 Department of Mathematics
 Synopsis:

Linear and nonlinear differential equations of the first order. Linear differential equations of higher order with constant coefficients. Multivariable calculus and its applications.
 Requirements:

Basis course in single variable calculus and linear algebra (in the extent of the courses at FNSPE, CTU in Prague: 01MAT1, 01MAT2, 01MAT3).
 Syllabus of lectures:

1. Linear differential equations of the first order 2. Nonlinear differential equation of the first order 3. Exact and homogeneous equations. 4. Linear differential equations of higher order 5. Linear differential equation with constant coefficients 6. Quadratic forms 7. Limit and continuity of multivariable functions 8. Multivariable calculus 9. Total differential 10. Implicit function 11. Change of variables 12. Extreme values of multivariable functions 13. Multidimensional Riemann integral 14. Fubini theorem and substitution theorem.
 Syllabus of tutorials:

1. Linear differential equations of the first order 2. Nonlinear differential equation of the first order 3. Linear differential equations of higher order 4. Linear differential equation with constant coefficients 5. Limit and continuity of multivariable functions 6. Implicit function 7. Extreme values of multivariable functions 8. Multidimensional Riemann integral 9. Fubini theorem and substitution theorem.
 Study Objective:

Knowledge: To learn how to solve some elementary classes of differential equations, especially LDE. To become familiar with multivariable calculus.
Abilities: To apply the knowledge above to particular problems in engineering.
 Study materials:

key references:
[1] J. Marsden, A. Weinstein: Calculus III, Springer, 1985.
recommneded references:
[2] W. Rudin: Principles of Mathematical Analysis, McGrawHill, 1976.
[3] J. Stewart: Multivariable Calculus, 8th Edition, Brooks Cole, 2015.
 Note:
 Further information:
 http://kmlinux.fjfi.cvut.cz/~tusekmat/index.php?str=forstudents
 Timetable for winter semester 2023/2024:
 Timetable is not available yet
 Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

 BS Aplikovaná informatika (compulsory course of the specialization)
 BS Jaderné inženýrství C (compulsory course of the specialization)
 BS Jaderná chemie (compulsory course of the specialization)
 Aplikovaná informatika (compulsory course in the program)
 Jaderná chemie (compulsory course in the program)
 Radiologická technika (compulsory course in the program)