714-0567/03 – Bachelor Mathematics II (BM II)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | RNDr. Zbyněk Urban, Ph.D. | Subject version guarantor | RNDr. Zbyněk Urban, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | English |
| Year of introduction | 2016/2017 | Year of cancellation | 2019/2020 |
| Intended for the faculties | HGF | Intended for study types | Bachelor, Follow-up Master |
Subject aims expressed by acquired skills and competences
Mathematics is 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
analyze problems, distinguish between important and unimportant, suggest a
method of solution, verify each step of a method, generalize achieved results,
analyze 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
Lectures
Individual consultations
Tutorials
Other activities
Summary
The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three advanced parts of mathematics, according to which the learning material is structured. In Integral Calculus, the main motive is the preparation to general use of definite and indefinite integrals of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Differential Equations is an emphasis on interpretation of the basic procedures for the solution of selected types of differential equations.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Tests and credits
=================
Exercises
---------
Conditions for obtaining credit points (CP):
- participation in exercises, 20% can be to apologize
- completion of three written tests, 0-15 CP
- completion of two programs, 5 CP
Exam
----
- written exam 0-60 CP, successful completion at least 25 CP
- oral exam 0-20 CP, successful completion at least 5 CP
Set of questions
-------------
The primitive function, indefinite integral, integration of elementary functions.
Integration by parts.
Integration by substitution.
Integration of rational functions.
Integration of trigonometric functions.
Integrating irrational functions.
Definite integral, definition and properties.
Calculation of a definite integral using integration by parts.
The calculation of definite integral by substitution.
Calculation of the area.
Calculation of the length of curves.
Calculation of the volume of the rotating body.
The definition of functions of two variables.
Partial derivatives.
The equation of the tangent plane and normal to surfaces.
Extrema of functions of two variables.
Implicit function and its derivatives.
Differential equations of the 1st order, general and particular solutions.
Separable differential equations.
Homogeneous differential equations.
Linear differential equation of the first order.
Linear differential equations with constant coefficients of the 2nd order - variation of constants.
Linear differential equations with constant coefficients of the 2nd order - determinaton of coefficients.
E-learning
Other requirements
No more reqieremwents
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Week. Lecture
-------------
1st Integral calculus: antiderivative and indefinite integral for functions of one variable.
2nd Integration methods - substitution, integration by parts.
3rd Integration of rational functions, irrational functions, trigonometric functions.
4th Definite integrals: basic concepts, properties, Newton-Leibniz rule.
5th Substitution method and integration by parts for the definite integral.
6th Applications of integrals in geometry.
7th Differential calculus for functions of two variables: definition, domain, limits and continuity.
8th Partial derivatives of first order and higher orders. Total differential.
9th The equation of the tangent plane and of the normal.
10th Extrema of functions of two variables.
11th Implicit function and its derivatives.
12th Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear.
13th Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients.
14th Linear differential equations of higher orders.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.