714-0237/01 – Repetition of Mathematics 2 (Repet 2)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 1 |
| Subject guarantor | doc. RNDr. Pavel Kreml, CSc. | Subject version guarantor | doc. RNDr. Pavel Kreml, CSc. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | 2 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2014/2015 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FAST | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is an essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.
Students should learn
how to analyse problems,
distinguish between important and unimportant,
suggest a method of solution,
verify each step of a method,
generalize achieved results,
analyse correctness of achieved results with respect to given conditions,
apply these methods while solving technical problems,
understand that mathematical methods and theoretical advancements outreach the field mathematics.
Teaching methods
Individual consultations
Tutorials
Summary
Repetition of Mathematics 2 is intended for students who, for whatever reasons,
fail the exam of Mathematics II and are interested in passing this exam. Its content essentially coincides with the content of the course Mathematics I. The aim is to enable better understanding of mathematics by the solving of concrete examples and problems. Repetition will focus on the practical part of the exam and they will be solved examples matching the written part of the exam.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
The course is optional and requires the active participation of students registered. Participation on tutorials is obligatory, 20% of absence can be apologized, elaborate programs.
E-learning
http://www.studopory.vsb.cz
http://mdg.vsb.cz
(in Czech language)
Other requirements
There are not additional requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Syllabus of tutorial
1. Course of a function of one real variable.
2. Integration by a direct method. Integration by substitution.
3. Integration by substitution. Integration by parts.
4. Integration of rational functions.
5. 1st test (basic methods of integration). Definite integrals.
6. Applications of definite integrals.
7. Functions of more variables, domain, partial derivatives.
8. Equation of a tangent plane and a normal to a graph of functions of two variables. Derivation of implicit functions.
9. Extrema of functions. 2nd test (functions of two variables).
10. Differential equations, separable and homogeneous differential equations.
11. Linear differential equations of 1st order. Exact differential equations.
12. 2nd order linear differential equations with constant coefficients.
13. Method of undetermined coefficients. 3rd test (differential equations).
14. Reserve.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction