Integral Calculus

Grading of the course requires grading of the following courses:

Linear Algebra and Differential Calculus (17BILAD)

Lecturer:

Marcel Jiřina (gar.)

Tutor:

Marcel Jiřina (gar.), Dagmar Brechlerová

Supervisor:

Department of Biomedical Informatics

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 transformation, Laplace transformation. Fourier series and Fourier transformation.

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]Frank Ayres, Elliott Mendelson: Theory and Problems of

Differential and Integral Calculus, Schaums Outline Series,

1990

[2]Edmund Landau: Differential and Integral Calculus, AMS

Chelsea Publishing, 2001

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

	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	roomKL:C-1 Jiřina M. 14:00–15:50 (lecture parallel1) Kladno FBMI Velký sál
Fri	roomKL:B-309 Brechlerová D. 10:00–11:50 (lecture parallel1 parallel nr.1) Kladno FBMI zasedačkaroomKL:GDM6_20 Brechlerová D. 12:00–13:50 (lecture parallel1 parallel nr.2) Kladno FBMI Učebna GDM6_20
Thu
Fri

The course is a part of the following study plans:

• Bakalářský studijní obor Biomedicínská informatika - prezenční (compulsory course)
• Bakalářský studijní obor Biomedicínská informatika - prezenční (compulsory course)