Mathematics 2
Code  Completion  Credits  Range  Language 

101MT02  Z,ZK  6  2P+3C 
 Grading of the course requires grading of the following courses:
 Mathematics 1 (101MT01)
 Lecturer:
 František Bubeník
 Tutor:
 Yuliya Namlyeyeva (guarantor), František Bubeník
 Supervisor:
 Department of Mathematics
 Synopsis:

1. Indefinite integral, primitive functions, tabular integrals. Fundamental methods for calculating indefinite
integrals: per partes, substitutions.
2. Integration of rational functions (with simple imaginary roots in denominators at most one).
3. Selected special substitutions.
4. Definite integral, fundamental methods for calculating definite integrals: Newton Leibniz`s formula, per partes,
substitutions.
5. Improper integrals, convergence and divergence of improper integrals, methods of computation.
6. Geometrical and physical applications of integral calculus : area of a plane figure, volume of a solid of revolution,
length of the graph of a function, static moments and the centre of gravity of a plane figure.
7. Functions of several variables. Definition domains, in case of two variables also level curves and graphs. Partial
derivatives, partial derivatives of higher orders.
8. Directional derivatives. Gradient. Total differential. Derivatives and partial derivatives of functions defined
implicitly.
9. Equations of tangent and normal lines of a plane curve and tangent planes and normal lines of a surface.
10. Local extrema and local extrema with respect to a set (constrained extrema).
11. Global extrema on a set.
12. Differential equations of the 1st order, separation of variables, homogeneous equations. Cauchy problems.
13. Linear differential equations of the 1st order, variation of a constant. Exact equations. Cauchy problems.
 Requirements:

Successfully passed exam for MAT1 (101MT01).
 Syllabus of lectures:

Integral calculus:
1. Indefinite integral, primitive functions, tabular integrals. Fundamental methods for calculating indefinite integrals: per partes, substitutions.
2. Integration of rational functions (with simple imaginary roots in denominators at most one).
3. Select special substitutions.
4. Definite integral, fundamental methods for calculating definite integrals: NewtonLeibniz's formula, per partes, substitutions.
5. Improper integrals, convergence and divergence of improper integrals, methods of computation.
6. Geometrical and physical applications of integral calculus: area of a plane figure (plane sheet), volume of a solid of revolution, length of the graph of a function, static moments and the centre of gravity of a plane figure.
Functions of more variables:
7. Domains of definitions, in case of two variables also level curves and graphs. Partial derivatives, partial derivatives of higher orders.
8. Directional derivatives. Gradient. Total differential. Derivatives and partial derivatives of functions defined implicitly.
9. Equations of tangent and normal lines of a plane curve and tangent planes and normal lines of a surface.
10. Local extremes and local extremes with respect to a set (constrained extremes).
11. Global extremes on a set.
Differential equations:
12. Differential equations of the 1st order, separation of variables, homogeneous equations. Cauchy problems.
13. Linear differential equations of the 1st order, variation of a constant. Exact equations. Cauchy problems.
 Syllabus of tutorials:

In general the exercises at each tutorial are based on the subject matter of the previous lecture.
 Study Objective:

The course is based on the knowledge learnt at course of Mathematics 1. Topics include extension of methods of calculus to functions of two or more variables, the concepts of antiderivatives and ordinary differential equations.
 Study materials:

!Bubeník F.: Mathematics for Engineers, Prague, 2014, ISBN 9788001056202
!Bubeník F.: Problems to Mathematics for Engineers, Prague, 2014, ISBN 9788001056219
!Rektorys K.: Survey of Applicable Mathematics, Vol. I, II, ISBN 9401583080, 9789401583084
 Note:
 Timetable for winter semester 2019/2020:
 Timetable is not available yet
 Timetable for summer semester 2019/2020:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri  The course is a part of the following study plans:

 Building Structures (compulsory course)
 Building Structures (compulsory course)
 Building Structures (compulsory course)