3.1 Thematic plan of modules

No.

Title of the theme

Form of conducting

hours

Code of LO

Module 1. Indefinite integral of a function of one variable. Methods of calculating of indefinite integrals.

3.1.1 Themes of lectures

1

1.Antiderivative functions. Definition and properties of indefinite integral. Table of basic integrals. Propeties of indefinite integral.

Introductionlecture

2

А1

B1

Е1

2

2. Integration by changing variable.

Reviewlecture

2

А2

B1

C1

3

3. Integration by parts

Lectureinformation

2

А1

B2.

D1

4

4. Integration of rational functions. Long division of polynomials. Partial fractions. Decomposition of rational function into a sum of partial fractions.

Lectureinformation

2

А1.

B3.

C1

5

5. Integration of some classes of trigonometric functions. General chang of variable .Chanf of variable . Change of variables and More techniques for integration of trigonometric expressions.

Problemlecture

2

А2.

B2.

Е2

6. Integration of irrational functions. Primatives of the form .

Trigonometric substitutions. Primatives of the form , where is not a perfect square.

Lectureinformation

2

B3.

C3

7

7. Primatives of the form where m, n, p are nonzero rational numbers and .

Lecture with a pre-scheduled errors

2

А1.

B3.

C3

Total for lectures:

14

3.1.2 Themes of practical

1

1.Antiderivative functions. Definition and properties of indefinite integral. Table of basic integrals. Propeties of indefinite integral.

Solving of the tasks

2

А1.

С2.

Е2

2

2. Integration by changing variable.

Business game

2

А1.

С2.

D1

3

3. Integration by parts

Solving of the tasks

2

А1.

С3.

D2

4

4. Integration of rational functions. Long division of polynomials. Partial fractions. Decomposition of rational function into a sum of partial fractions.

Solving of the tasks

2

А1.

B2.

D3

5

5. Integration of some classes of trigonometric functions. General chang of variable .Chanf of variable . Change of variables and More techniques for integration of trigonometric expressions.

problem method

2

А1.

B3.

D3

6

6. Integration of irrational functions. Primatives of the form .

Trigonometric substitutions. Primatives of the form , where is not a perfect square.

Solving of the tasks

2

А1.

B3.

Е2

7

7. Primatives of the form where m, n, p are nonzero rational numbers and .

interdisciplinary training

2

Total for practical classes

14

Total for the 1^st Module

28

Module 2. Definite integral of a function of one variable. Methods of calculating of definite integrals.

3.1.5Lecture themes

1

8. Definition of a definite integral. . Mean theorem. Newton-Leibniz formula.

Lectureinformation

2

А2.

С1.

D3

2

9. Methods of calculating definite integrals. Integration by changing variable.

Lecture – talk

2

А3.

С2.

Е3

3

10. Integration by parts

Lectureinformation

2

А3.

С3.

Е3

4

11. Applications of a definite integral. Area of a plane region.

Lectureinformation

2

А1.

B2.

C3

5

12. Length of a Plane Curve

Lectureinformation

2

B1.

С2.

D3

6

13. Volume of a Rotational solid

LectureConsultation

2

B1.

С2.

D3

7

14. Area of a rotational Surface

Lecture – talk

2

B2.

С3.

D3

8

15. Improrer integral.

Lectureinformation

2

B2.

С3.

D3

Total for lectures:

16

Themes of practical /classes

1

8. Definition of a definite integral. . Mean theorem. Newton-Leibniz formula.

Solving of the tasks

2

А1.

С2.

Е3

2

9. Methods of calculating definite integrals. Integration by changing variable.

Solving of the tasks

2

А2.

С2.

B3

3

10. Integration by parts

Solving of the tasks

2

B1.

С2.

Е3

4

11. Applications of a definite integral. Area of a plane region.

Solving of the tasks

2

B1.

С1.

D3

5

12. Length of a Plane Curve

problem method

2

B1.

С2.

D3

6

13. Volume of a Rotational solid

interdisciplinary training

2

А2.

С2.

Е3

7

14. Area of a rotational Surface

interdisciplinary training

2

А1.

С3.

Е1

8

15. Improrer integral.

individual   training

2

А1.

С3.

Е1

Total for practical classes

16

Total for the 2^nd module:

32

Total for the subject:

60