Mathematics 4

Garant předmětu:

Leopold Vrána

Lecturer:

Leopold Vrána

Tutor:

Leopold Vrána

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:

[1] J. Marsden, A. Weinstein: Calculus III, Springer, 1985.

recommneded references:

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

[3] 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 2022/2023:

Time-table is not available yet

Time-table for summer semester 2022/2023:

Time-table 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 Radiologická technika (compulsory course of the specialization)
• Bc Laser Technology and Instrumentation (compulsory course of the specialization)
• BS Fyzikální technika (compulsory course of the specialization)
• BS Jaderná chemie (compulsory course of the specialization)