 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Mathematics 4

Code Completion Credits Range Language
01MAT4 Z,ZK 4 2+2 Czech
Lecturer:
Matěj Tušek (guarantor)
Tutor:
Matěj Tušek (guarantor), Jiří Franc
Supervisor:
Department of Mathematics
Synopsis:

Linear and non-linear 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. Non-linear 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. Non-linear 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:

 J. Marsden, A. Weinstein: Calculus III, Springer, 1985.

recommneded references:

 W. Rudin: Principles of Mathematical Analysis, McGraw-Hill, 1976.

 J. Stewart: Multivariable Calculus, 8th Edition, Brooks Cole, 2015.

Note:
Further information:
http://kmlinux.fjfi.cvut.cz/~tusekmat/index.php?str=forstudents
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-07-07
For updated information see http://bilakniha.cvut.cz/en/predmet11278405.html