Integral Calculus

Grading of the course requires grading of the following courses:

Linear Algebra and Differential Calculus (17ABBLAD)

Lecturer:

Tutor:

Supervisor:

Department of Natural Sciences

Synopsis:

Definite and indefinite integral, methods of solutions, applications of definite integral for area/volume under curve, volumes and areas of rotational bodies, static moments and centers of gravity. Differential and difference equations and methods of their solution. Integral transforms, Laplace transform, Z transform.

Requirements:

Credit inclusion: Maximal 2 cuts, maximal 2 excused absenteeisms.

Exam: Written and oral.

Syllabus of lectures:

1. Introduction to indefinite integral, basic features, per partes, substitution, integration of racinal functions, partial fraction decomposition

2. Introduction to definite integral, improper integral

3. Application of integrals, area, moment, center of gravity

4. Solving of differential equations, separation of variables, solving of homogenious differential equations and variation of constants for linear differential equations

5. Integral transform, Laplace transform

6. Use of Laplace transform for solving of differential equations

7. Discretization of Laplace transform, Z-transform

8. Use of Z-transform for solving linear difference equations

9. Double integral, introduction and direct methods od its solving

10. Jacobian and substitution in double integral, polar coordinates

11. Physical and geometric application od double integral

12. Fourier series and Fourier transform, basic features, convolution

13. Use if Fourier transform

14. Reserve

Syllabus of tutorials:

The practical training course reflects theoretical knowledge of lectures. The outline is similar to the outline of lectures.

Study Objective:

The goal of the subject is to introduce students to basics of integral calculus and its application. The students should be able to solve definite and indefinite integrals, operate with Laplace and Z transformation and solve differential and difference equation.

Study materials:

1.Tkadlec, J.: Diferenciální a integrální počet funkcí jedné proměnné, skriptum FEL ČVUT

2.Neustupa J., Kračmar, S.: Sbírka příkladů z Matematiky I., skriptum FS ČVUT

3.Neustupa J.: Matematika I, skriptum FS ČVUT

4.Hamhalter, J., Tišer J.: Integrální počet funkcí více proměnných, FEL ČVUT

5.Hamhalter, J., Tišer J.: Difereciální počet funkcí více proměnných, FEL ČVUT

6.Tkadlec, J.: Diferenciální rovnice, Laplaceova transformace, skriptum FEL ČVUT

7.Průcha L.: Řady, skriptum FEL ČVUT

8.Brožíková, E. a Kittlerová, M.: Sbírka příkladů z matematiky II, skriptum FS ČVUT

9.Čipera, S.: Řešené příklady z matematiky 3, skriptum FS ČVUT

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Bakalářský studijní obor Biomedicínský technik v AJ (compulsory course)